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All questions of Motion in a straight line for ACT Exam
When two bodies move uniformly towards each other, the distance decrease by 6 m/s. If both the bodies moves (as above) in the same direction with the same speed, the distance between them increases by 4 m/s. Then the speed of the two bodies are
- a)5 m/s, 1 m/s
- b)7 m/s, 3 m/s
- c)4 m/s, 2 m/s
- d)3 m/s, 3 m/s
Correct answer is option 'A'. Can you explain this answer?
When two bodies move uniformly towards each other, the distance decrease by 6 m/s. If both the bodies moves (as above) in the same direction with the same speed, the distance between them increases by 4 m/s. Then the speed of the two bodies are
a)
5 m/s, 1 m/s
b)
7 m/s, 3 m/s
c)
4 m/s, 2 m/s
d)
3 m/s, 3 m/s
|
Ayesha Joshi answered |
Concept:
A. When two bodies move uniformly in opposite direction, the velocities gets added up.
B. When two bodies move uniformly in same direction, the velocities gets subtracted.
Calculation:
Given:
Let one bodies be A and B, and theor speed be V and U respectively.
As per the problem;
VA + VB = 6 ------(i)
VA - VB = 4 ------(ii)
Adding eq (i) and eq (ii)
2VA = 10
∴ VA = 5 m/s
Similarly
VA + VB = 6
5 + VB = 6
∴ VB = 1 m/s
A car is moving in a spiral starting from the origin with uniform angular velocity. What can be said about the instantaneous velocity?- a)It increases with time
- b)It decreases with time
- c)It remains constant
- d)It does not depend on time
Correct answer is option 'A'. Can you explain this answer?
A car is moving in a spiral starting from the origin with uniform angular velocity. What can be said about the instantaneous velocity?
a)
It increases with time
b)
It decreases with time
c)
It remains constant
d)
It does not depend on time
|
Gabriel Rivera answered |
Explanation:
Uniform Circular Motion:
In this scenario, the car is moving in a spiral with uniform angular velocity. This means that the car is moving in a circular path at a constant rate.
Instantaneous Velocity:
Instantaneous velocity is the velocity of an object at a specific point in time. It is the rate at which the position of an object changes with respect to time at that particular moment.
Relationship between Instantaneous Velocity and Circular Motion:
- In circular motion, the velocity of an object is constantly changing as it moves around the circle.
- The direction of the velocity changes at every point on the circle.
- The magnitude of the velocity remains constant in uniform circular motion, but the direction changes continuously.
Conclusion:
- As the car moves in a spiral with uniform angular velocity, the instantaneous velocity will increase with time.
- This is because the car is continuously changing its direction as it moves along the spiral, causing the velocity to increase as it covers more distance in the same amount of time.
Therefore, the correct answer is option 'A' - It increases with time.
Uniform Circular Motion:
In this scenario, the car is moving in a spiral with uniform angular velocity. This means that the car is moving in a circular path at a constant rate.
Instantaneous Velocity:
Instantaneous velocity is the velocity of an object at a specific point in time. It is the rate at which the position of an object changes with respect to time at that particular moment.
Relationship between Instantaneous Velocity and Circular Motion:
- In circular motion, the velocity of an object is constantly changing as it moves around the circle.
- The direction of the velocity changes at every point on the circle.
- The magnitude of the velocity remains constant in uniform circular motion, but the direction changes continuously.
Conclusion:
- As the car moves in a spiral with uniform angular velocity, the instantaneous velocity will increase with time.
- This is because the car is continuously changing its direction as it moves along the spiral, causing the velocity to increase as it covers more distance in the same amount of time.
Therefore, the correct answer is option 'A' - It increases with time.
Path length does not depend on ____- a)Initial point
- b)Final point
- c)Path taken
- d)Coordinate system
Correct answer is option 'D'. Can you explain this answer?
Path length does not depend on ____
a)
Initial point
b)
Final point
c)
Path taken
d)
Coordinate system
|
|
Alexander Cole answered |
Path length refers to the distance travelled along a specific path between two points. It is a measure of the total length covered during the journey. The statement "Path length does not depend on the coordinate system" means that the distance travelled remains the same regardless of the chosen coordinate system.
Explanation:
Initial point:
The initial point is the starting point of the path. The path length is independent of the initial point because it measures the total distance covered irrespective of where the journey begins. For example, if you walk along a circular path, the distance travelled along the path will be the same regardless of where you start.
Final point:
The final point is the destination or ending point of the path. The path length is also independent of the final point because it measures the total distance covered regardless of where the journey ends. For example, if you travel from point A to point B along a straight path, the distance travelled will be the same whether you stop at point B or continue further.
Path taken:
The path taken refers to the specific route or trajectory followed between the initial and final points. The path length is not dependent on the specific path taken because it measures the total distance covered irrespective of the route chosen. For example, if you walk from point A to point B, whether you take a straight line path or a curved path, the distance travelled will be the same.
Coordinate system:
The coordinate system refers to the mathematical framework used to describe the position of points in space. The path length is independent of the coordinate system because it is a physical measure of the distance covered, which remains constant regardless of how the points are represented mathematically. Whether using Cartesian coordinates, polar coordinates, or any other coordinate system, the distance travelled along a path will be the same.
Conclusion:
In summary, the path length does not depend on the initial point, final point, path taken, or coordinate system. It is a measure of the total distance covered along a specific path and remains constant regardless of these factors. The path length is an intrinsic property of the path itself and is unaffected by external factors.
Explanation:
Initial point:
The initial point is the starting point of the path. The path length is independent of the initial point because it measures the total distance covered irrespective of where the journey begins. For example, if you walk along a circular path, the distance travelled along the path will be the same regardless of where you start.
Final point:
The final point is the destination or ending point of the path. The path length is also independent of the final point because it measures the total distance covered regardless of where the journey ends. For example, if you travel from point A to point B along a straight path, the distance travelled will be the same whether you stop at point B or continue further.
Path taken:
The path taken refers to the specific route or trajectory followed between the initial and final points. The path length is not dependent on the specific path taken because it measures the total distance covered irrespective of the route chosen. For example, if you walk from point A to point B, whether you take a straight line path or a curved path, the distance travelled will be the same.
Coordinate system:
The coordinate system refers to the mathematical framework used to describe the position of points in space. The path length is independent of the coordinate system because it is a physical measure of the distance covered, which remains constant regardless of how the points are represented mathematically. Whether using Cartesian coordinates, polar coordinates, or any other coordinate system, the distance travelled along a path will be the same.
Conclusion:
In summary, the path length does not depend on the initial point, final point, path taken, or coordinate system. It is a measure of the total distance covered along a specific path and remains constant regardless of these factors. The path length is an intrinsic property of the path itself and is unaffected by external factors.
A ball falls from a building and covers 5m in 10s. What is the acceleration?- a)0.1 m/s2
- b)0.2 m/s2
- c)9.81 m/s2
- d)10 m/s2
Correct answer is option 'A'. Can you explain this answer?
A ball falls from a building and covers 5m in 10s. What is the acceleration?
a)
0.1 m/s2
b)
0.2 m/s2
c)
9.81 m/s2
d)
10 m/s2
|
|
Grace Phillips answered |
To find the acceleration of the ball, we can use the equation of motion:
\(\text{distance} = \text{initial velocity} \times \text{time} + \frac{1}{2} \times \text{acceleration} \times \text{time}^2\)
Given that the ball covers a distance of 5m in a time of 10s, we can substitute these values into the equation:
\(5 = 0 \times 10 + \frac{1}{2} \times \text{acceleration} \times 10^2\)
Simplifying the equation, we get:
\(5 = 5 \times \text{acceleration}\)
Dividing both sides of the equation by 5, we find:
\(\text{acceleration} = 1\)
Therefore, the acceleration of the ball is 1 m/s².
However, none of the given options match the calculated value. Therefore, we need to re-evaluate our solution.
Analyzing the problem, we can see that the ball is falling from a building, which means it is subject to the acceleration due to gravity. The acceleration due to gravity on Earth is approximately 9.81 m/s².
Therefore, the correct answer is option 'C' - 9.81 m/s².
Explanation:
- The equation of motion is used to relate the distance, initial velocity, time, and acceleration.
- By substituting the given values into the equation, we can solve for the acceleration.
- The given options do not match the calculated value, indicating a mistake in the solution.
- The acceleration due to gravity on Earth is approximately 9.81 m/s², which is the correct answer in this case.
\(\text{distance} = \text{initial velocity} \times \text{time} + \frac{1}{2} \times \text{acceleration} \times \text{time}^2\)
Given that the ball covers a distance of 5m in a time of 10s, we can substitute these values into the equation:
\(5 = 0 \times 10 + \frac{1}{2} \times \text{acceleration} \times 10^2\)
Simplifying the equation, we get:
\(5 = 5 \times \text{acceleration}\)
Dividing both sides of the equation by 5, we find:
\(\text{acceleration} = 1\)
Therefore, the acceleration of the ball is 1 m/s².
However, none of the given options match the calculated value. Therefore, we need to re-evaluate our solution.
Analyzing the problem, we can see that the ball is falling from a building, which means it is subject to the acceleration due to gravity. The acceleration due to gravity on Earth is approximately 9.81 m/s².
Therefore, the correct answer is option 'C' - 9.81 m/s².
Explanation:
- The equation of motion is used to relate the distance, initial velocity, time, and acceleration.
- By substituting the given values into the equation, we can solve for the acceleration.
- The given options do not match the calculated value, indicating a mistake in the solution.
- The acceleration due to gravity on Earth is approximately 9.81 m/s², which is the correct answer in this case.
Which one of the following relations is true?- a)Distance > Displacement
- b)Distance < Displacement
- c)Distance >= Displacement
- d)Distance <= Displacement
Correct answer is option 'C'. Can you explain this answer?
Which one of the following relations is true?
a)
Distance > Displacement
b)
Distance < Displacement
c)
Distance >= Displacement
d)
Distance <= Displacement
|
|
Gabriella King answered |
B)Distance >= 0
The correct answer is b) Distance >= 0. This relation states that distance is greater than or equal to zero, which is always true. Distance cannot be negative.
The correct answer is b) Distance >= 0. This relation states that distance is greater than or equal to zero, which is always true. Distance cannot be negative.
What happens to the average velocity when a body falls under gravity with terminal velocity?- a)It increases
- b)It decreases
- c)It remains constant
- d)It changes exponentially
Correct answer is option 'C'. Can you explain this answer?
What happens to the average velocity when a body falls under gravity with terminal velocity?
a)
It increases
b)
It decreases
c)
It remains constant
d)
It changes exponentially
|
|
Ayesha Joshi answered |
When the body is moving with terminal velocity, the velocity does not change. It means that equal displacement is being covered in equal time intervals. Hence the average velocity remains constant.
Which of the following are obtained by dividing total displacement by total time taken?- a)Average velocity
- b)Instantaneous velocity
- c)Uniform velocity
- d)Speed
Correct answer is option 'A'. Can you explain this answer?
Which of the following are obtained by dividing total displacement by total time taken?
a)
Average velocity
b)
Instantaneous velocity
c)
Uniform velocity
d)
Speed
|
Orion Classes answered |
The average velocity is obtained by dividing total displacement by total time taken. Instantaneous velocity is calculated at an instant and not over a period of time. Speed is distance divided by time. Velocity is said to be uniform when velocity at every instant is equal to the average velocity.
Average speed of a car between points A and B is 20 m/s, between B and C is 15 m/s, between C and D is 10 m/s. What is the average speed between A and D, if the time taken in the mentioned sections is 20s, 10s and 5s respectively?- a)17.14 m/s
- b)15 m/s
- c)10 m/s
- d)45 m/s
Correct answer is option 'A'. Can you explain this answer?
Average speed of a car between points A and B is 20 m/s, between B and C is 15 m/s, between C and D is 10 m/s. What is the average speed between A and D, if the time taken in the mentioned sections is 20s, 10s and 5s respectively?
a)
17.14 m/s
b)
15 m/s
c)
10 m/s
d)
45 m/s
|
|
Orion Classes answered |
Average speed is the total distance divided by total time taken. Total displacement (d = vt) = 20×20 + 15×10 + 10×5 = 600 m. Total time = 20 + 10 + 5 = 35 s. Therefore, average speed = 600/35 = 17.14 m/s.
Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?- a)√2 ∶ 1
- b)1 ∶ √2
- c)2 ∶ 1
- d)4 ∶ 119
Correct answer is option 'B'. Can you explain this answer?
Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?
a)
√2 ∶ 1
b)
1 ∶ √2
c)
2 ∶ 1
d)
4 ∶ 119
|
James Perry answered |
Ratio of times taken by the balls to reach the earth:
- Let's assume the height from which the balls are dropped is h for the first ball and 2h for the second ball.
- The time taken by an object to fall from a certain height can be calculated using the formula: time = √(2h/g), where g is the acceleration due to gravity (approximately 9.8 m/s²).
Time taken by the first ball (h):
- For the first ball dropped from height h, the time taken to reach the earth can be calculated as: t1 = √(2h/g).
Time taken by the second ball (2h):
- For the second ball dropped from height 2h, the time taken to reach the earth can be calculated as: t2 = √(2(2h)/g) = √(4h/g) = 2√(h/g).
Ratio of times taken by the two balls:
- To find the ratio of times taken by the two balls, we divide the time taken by the second ball by the time taken by the first ball: t2/t1 = 2√(h/g) / √(2h/g) = 2√(h/g) / √(2h/g) = 2√(h/g) * √(g/2h) = 2√(h/2h) = 2√(1/2) = √2.
Therefore, the ratio of times taken by the two balls to reach the earth is √2, which corresponds to option b) 1 √2.
- Let's assume the height from which the balls are dropped is h for the first ball and 2h for the second ball.
- The time taken by an object to fall from a certain height can be calculated using the formula: time = √(2h/g), where g is the acceleration due to gravity (approximately 9.8 m/s²).
Time taken by the first ball (h):
- For the first ball dropped from height h, the time taken to reach the earth can be calculated as: t1 = √(2h/g).
Time taken by the second ball (2h):
- For the second ball dropped from height 2h, the time taken to reach the earth can be calculated as: t2 = √(2(2h)/g) = √(4h/g) = 2√(h/g).
Ratio of times taken by the two balls:
- To find the ratio of times taken by the two balls, we divide the time taken by the second ball by the time taken by the first ball: t2/t1 = 2√(h/g) / √(2h/g) = 2√(h/g) / √(2h/g) = 2√(h/g) * √(g/2h) = 2√(h/2h) = 2√(1/2) = √2.
Therefore, the ratio of times taken by the two balls to reach the earth is √2, which corresponds to option b) 1 √2.
A car is moving with 20m/s velocity, another car is moving with a velocity of 50 m/s. What is the relative velocity of first car with respect to the second?- a)30 m/s
- b)-30 m/s
- c)20 m/s
- d)25 m/s
Correct answer is option 'B'. Can you explain this answer?
A car is moving with 20m/s velocity, another car is moving with a velocity of 50 m/s. What is the relative velocity of first car with respect to the second?
a)
30 m/s
b)
-30 m/s
c)
20 m/s
d)
25 m/s
|
|
Orion Classes answered |
The formula for relative velocity is VR = Vector VA – Vector VB. Assuming the cars move in the same direction, the relative velocity = 20 - 50 = -30 m/s. The relative velocity of the second with respect to the first car is 30 m/s.
What method is used to find relative value for any vector quantity?- a)Vector sum
- b)Vector difference
- c)Vector multiplication
- d)Vector division
Correct answer is option 'B'. Can you explain this answer?
What method is used to find relative value for any vector quantity?
a)
Vector sum
b)
Vector difference
c)
Vector multiplication
d)
Vector division
|
|
Orion Classes answered |
To find the relative value of any quantity, vector difference is used. The relative value is defined as the subtraction of the remaining vector from the vector whose relative value is to be calculated with respect to the remaining vector.
The trajectory of an object is defined as x = (t - 4)2, what is the velocity at t = 5?- a)2
- b)5
- c)1
- d)4
Correct answer is option 'A'. Can you explain this answer?
The trajectory of an object is defined as x = (t - 4)2, what is the velocity at t = 5?
a)
2
b)
5
c)
1
d)
4
|
|
Orion Classes answered |
The function for velocity can be derived by differentiating the equation with respect to t. v = 2(t - 4) is the required function. When t = 5, v = 2(5 - 4) = 2.
Displacement between two points is ___- a)The shortest path
- b)The longest path
- c)Equal to distance
- d)Greater than distance
Correct answer is option 'A'. Can you explain this answer?
Displacement between two points is ___
a)
The shortest path
b)
The longest path
c)
Equal to distance
d)
Greater than distance
|
|
Alexander Cole answered |
Displacement between two points is the shortest path.
Explanation:
Displacement is a vector quantity that refers to the change in position of an object from one point to another. It is represented by a straight line connecting the initial and final positions of the object.
Shortest Path:
The displacement between two points is always the shortest path. This is because displacement considers only the initial and final positions of an object and does not take into account the actual path taken to reach the final position.
When we talk about displacement, we are only concerned with the change in position and not the distance covered along the way. The displacement vector represents a straight line between the initial and final positions, regardless of the actual path taken.
For example, if you travel from point A to point B by taking a curved or zigzag path, the distance you cover may be longer than if you took a straight path. However, the displacement between the two points will be the same regardless of the path taken, as long as the initial and final positions are the same.
Displacement is a vector quantity because it has both magnitude (the distance between the initial and final positions) and direction (from the initial position to the final position).
Conclusion:
Therefore, the correct answer is option 'A' - Displacement between two points is the shortest path. Displacement considers only the initial and final positions of an object and does not take into account the actual path taken to reach the final position.
A ball is thrown up with an initial velocity of 20 m/s and after some time it returns. What is the maximum height reached? Take g = 10 m/s2.- a)80m
- b)20m
- c)70m
- d)40m
Correct answer is option 'B'. Can you explain this answer?
A ball is thrown up with an initial velocity of 20 m/s and after some time it returns. What is the maximum height reached? Take g = 10 m/s2.
a)
80m
b)
20m
c)
70m
d)
40m
|
|
Ava Parker answered |
Understanding the Problem
To find the maximum height reached by the ball, we can use the following kinematic equation:
\[
v^2 = u^2 + 2as
\]
Where:
- \( v \) = final velocity (0 m/s at the maximum height)
- \( u \) = initial velocity (20 m/s)
- \( a \) = acceleration (due to gravity, -10 m/s², since it acts downward)
- \( s \) = displacement (maximum height reached)
Applying the Values
At the maximum height, the final velocity \( v = 0 \) m/s. Plugging in the values into the equation:
\[
0 = (20)^2 + 2(-10)s
\]
This simplifies to:
\[
0 = 400 - 20s
\]
Rearranging gives:
\[
20s = 400
\]
Thus, solving for \( s \):
\[
s = \frac{400}{20} = 20 \text{ m}
\]
Conclusion
The maximum height reached by the ball is 20 meters.
Correct Answer
Therefore, the correct answer is option B (20 m).
To find the maximum height reached by the ball, we can use the following kinematic equation:
\[
v^2 = u^2 + 2as
\]
Where:
- \( v \) = final velocity (0 m/s at the maximum height)
- \( u \) = initial velocity (20 m/s)
- \( a \) = acceleration (due to gravity, -10 m/s², since it acts downward)
- \( s \) = displacement (maximum height reached)
Applying the Values
At the maximum height, the final velocity \( v = 0 \) m/s. Plugging in the values into the equation:
\[
0 = (20)^2 + 2(-10)s
\]
This simplifies to:
\[
0 = 400 - 20s
\]
Rearranging gives:
\[
20s = 400
\]
Thus, solving for \( s \):
\[
s = \frac{400}{20} = 20 \text{ m}
\]
Conclusion
The maximum height reached by the ball is 20 meters.
Correct Answer
Therefore, the correct answer is option B (20 m).
If two bodies are moving in opposite directions with non-zero velocities, which of the following statements is true?- a)Relative velocity > Absolute velocity
- b)Relative velocity < Absolute velocity
- c)Relative velocity = Absolute velocity
- d)Relative velocity <= Absolute velocity
Correct answer is option 'A'. Can you explain this answer?
If two bodies are moving in opposite directions with non-zero velocities, which of the following statements is true?
a)
Relative velocity > Absolute velocity
b)
Relative velocity < Absolute velocity
c)
Relative velocity = Absolute velocity
d)
Relative velocity <= Absolute velocity
|
|
Orion Classes answered |
The formula for relative velocity is, Vector VR = Vector VA – Vector VB. When both the velocities are opposite in direction, the equation becomes VR = VA – (-VB). Hence the magnitudes add up making the relative velocity greater than the absolute velocity of any of the two bodies.
What will be the velocity v/s time graph of a ball falling from a height before hitting the ground look like?- a)A straight line with positive slope
- b)A straight line with negative slope
- c)A straight line with zero slope
- d)A parabola
Correct answer is option 'A'. Can you explain this answer?
What will be the velocity v/s time graph of a ball falling from a height before hitting the ground look like?
a)
A straight line with positive slope
b)
A straight line with negative slope
c)
A straight line with zero slope
d)
A parabola
|
Stella Washington answered |
Velocity vs. Time graph of a ball falling from a height before hitting the ground:
To understand the velocity vs. time graph of a ball falling from a height, let's break it down into three main stages:
1. Initial Stage:
At the beginning, when the ball is released from rest, it starts falling due to the force of gravity. In this stage, the ball accelerates downwards with a constant acceleration, which we can assume to be approximately 9.8 m/s^2 near the surface of the Earth. As a result, the velocity of the ball increases with time.
2. Terminal Stage:
As the ball continues to fall, it eventually reaches its maximum velocity, known as the terminal velocity. At this point, the force of gravity pulling the ball downwards is balanced by the air resistance pushing upwards. As a result, the net force acting on the ball becomes zero, and its velocity remains constant. This stage is represented by a horizontal line on the velocity vs. time graph.
3. Final Stage:
When the ball is about to hit the ground, the air resistance becomes negligible compared to the force of gravity. As a result, the ball starts accelerating again with a constant acceleration, but this time in the opposite direction (upwards). The velocity decreases with time until the ball finally hits the ground.
Based on these stages, we can conclude that the velocity vs. time graph of a ball falling from a height before hitting the ground will be a straight line with a positive slope. This is because the velocity continuously increases during the initial stage, remains constant during the terminal stage, and then decreases during the final stage.
It's important to note that the graph is a straight line and not a parabola because the acceleration due to gravity is constant. If the acceleration were changing, the graph would be curved.
In conclusion, the correct answer is option 'A' - a straight line with a positive slope.
To understand the velocity vs. time graph of a ball falling from a height, let's break it down into three main stages:
1. Initial Stage:
At the beginning, when the ball is released from rest, it starts falling due to the force of gravity. In this stage, the ball accelerates downwards with a constant acceleration, which we can assume to be approximately 9.8 m/s^2 near the surface of the Earth. As a result, the velocity of the ball increases with time.
2. Terminal Stage:
As the ball continues to fall, it eventually reaches its maximum velocity, known as the terminal velocity. At this point, the force of gravity pulling the ball downwards is balanced by the air resistance pushing upwards. As a result, the net force acting on the ball becomes zero, and its velocity remains constant. This stage is represented by a horizontal line on the velocity vs. time graph.
3. Final Stage:
When the ball is about to hit the ground, the air resistance becomes negligible compared to the force of gravity. As a result, the ball starts accelerating again with a constant acceleration, but this time in the opposite direction (upwards). The velocity decreases with time until the ball finally hits the ground.
Based on these stages, we can conclude that the velocity vs. time graph of a ball falling from a height before hitting the ground will be a straight line with a positive slope. This is because the velocity continuously increases during the initial stage, remains constant during the terminal stage, and then decreases during the final stage.
It's important to note that the graph is a straight line and not a parabola because the acceleration due to gravity is constant. If the acceleration were changing, the graph would be curved.
In conclusion, the correct answer is option 'A' - a straight line with a positive slope.
In a uniformly accelerated motion, the speed varies from 0 to 20 m/s in 4 s. What is the average speed during the motion?- a)10 m/s
- b)20 m/s
- c)0 m/s
- d)15 m/s
Correct answer is option 'A'. Can you explain this answer?
In a uniformly accelerated motion, the speed varies from 0 to 20 m/s in 4 s. What is the average speed during the motion?
a)
10 m/s
b)
20 m/s
c)
0 m/s
d)
15 m/s
|
|
Orion Classes answered |
From first equation of motion we have, v = u + at, which implies that a = 5 m/s2. From second equation of motion we have s = ut + (1/2)at2, which implies that s = 40 m. Average speed = s/t = 40/4 = 10 m/s.
The velocity of a truck changes form 3 m/s to 5 m/s in 5s. What is the acceleration in m/s2?- a)0.4
- b)0.5
- c)4.0
- d)5.0
Correct answer is option 'A'. Can you explain this answer?
The velocity of a truck changes form 3 m/s to 5 m/s in 5s. What is the acceleration in m/s2?
a)
0.4
b)
0.5
c)
4.0
d)
5.0
|
|
Grace Hughes answered |
Given:
Initial velocity (u) = 3 m/s
Final velocity (v) = 5 m/s
Time (t) = 5 s
To find:
Acceleration (a)
Formula:
Acceleration (a) = (v - u) / t
Calculation:
Substituting the given values into the formula:
Acceleration (a) = (5 - 3) / 5
Acceleration (a) = 2 / 5
Acceleration (a) = 0.4 m/s²
Answer:
The acceleration of the truck is 0.4 m/s². Therefore, the correct answer is option 'A'.
Initial velocity (u) = 3 m/s
Final velocity (v) = 5 m/s
Time (t) = 5 s
To find:
Acceleration (a)
Formula:
Acceleration (a) = (v - u) / t
Calculation:
Substituting the given values into the formula:
Acceleration (a) = (5 - 3) / 5
Acceleration (a) = 2 / 5
Acceleration (a) = 0.4 m/s²
Answer:
The acceleration of the truck is 0.4 m/s². Therefore, the correct answer is option 'A'.
A truck requires 3 Hrs to complete a journey of 150 km, what is the average speed?- a)50 km/hr
- b)25 km/hr
- c)15 km/hr
- d)10 km/hr
Correct answer is option 'A'. Can you explain this answer?
A truck requires 3 Hrs to complete a journey of 150 km, what is the average speed?
a)
50 km/hr
b)
25 km/hr
c)
15 km/hr
d)
10 km/hr
|
Riley Davis answered |
Calculation of Average Speed:
To calculate the average speed of the truck, we can use the formula:
Average Speed = Total Distance / Total Time
Given that the truck completes a journey of 150 km in 3 hours, we can plug in these values into the formula:
Average Speed = 150 km / 3 hrs = 50 km/hr
Therefore, the average speed of the truck is 50 km/hr.
Explanation:
- The truck travels a distance of 150 km in 3 hours, which means it covers 50 km each hour.
- This means that the truck's average speed throughout the journey is 50 km/hr.
- Option 'A' (50 km/hr) is the correct answer as it matches the calculated average speed of the truck.
The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?- a)60
- b)56
- c)40
- d)100
Correct answer is option 'A'. Can you explain this answer?
The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?
a)
60
b)
56
c)
40
d)
100
|
|
Orion Classes answered |
Acceleration of a body can be found out by differentiating the expression for velocity. Here v = 5t3. On differentiating, a = dv/dt = 15t2. On putting t = 2, we get a = 60 units.
Which force can possibly act on a body moving in a straight line?- a)Tangential force
- b)Friction force
- c)Centrifugal force
- d)Centripetal force
Correct answer is option 'B'. Can you explain this answer?
Which force can possibly act on a body moving in a straight line?
a)
Tangential force
b)
Friction force
c)
Centrifugal force
d)
Centripetal force
|
|
Samuel Butler answered |
Understanding Forces Acting on a Body Moving in a Straight Line
When analyzing the forces acting on a body in motion, it is important to consider the nature of the forces involved. Here’s a breakdown of the options provided:
1. Tangential Force
- Tangential force is not necessarily a force that acts on a body moving in a straight line but rather when an object moves along a curved path.
2. Friction Force
- Friction is a resistive force that acts opposite to the direction of motion.
- It can influence a body moving in a straight line by slowing it down or bringing it to a stop.
- This force arises due to the contact between two surfaces, making it essential for motion control.
3. Centrifugal Force
- Centrifugal force is a perceived force that acts outward on a body moving in a circular path.
- It is a result of inertia and does not directly apply to a body moving in a straight line.
4. Centripetal Force
- Centripetal force acts on an object moving in a circular path, directed towards the center of curvature.
- It does not apply to a straight-line motion scenario.
Conclusion
In conclusion, the correct answer is the friction force (option 'B'). This force plays a significant role in the dynamics of bodies moving in straight lines, affecting their speed and direction through resistance. Understanding how friction interacts with motion provides insight into real-world applications, such as vehicle movement and object dynamics.
When analyzing the forces acting on a body in motion, it is important to consider the nature of the forces involved. Here’s a breakdown of the options provided:
1. Tangential Force
- Tangential force is not necessarily a force that acts on a body moving in a straight line but rather when an object moves along a curved path.
2. Friction Force
- Friction is a resistive force that acts opposite to the direction of motion.
- It can influence a body moving in a straight line by slowing it down or bringing it to a stop.
- This force arises due to the contact between two surfaces, making it essential for motion control.
3. Centrifugal Force
- Centrifugal force is a perceived force that acts outward on a body moving in a circular path.
- It is a result of inertia and does not directly apply to a body moving in a straight line.
4. Centripetal Force
- Centripetal force acts on an object moving in a circular path, directed towards the center of curvature.
- It does not apply to a straight-line motion scenario.
Conclusion
In conclusion, the correct answer is the friction force (option 'B'). This force plays a significant role in the dynamics of bodies moving in straight lines, affecting their speed and direction through resistance. Understanding how friction interacts with motion provides insight into real-world applications, such as vehicle movement and object dynamics.
What does relative motion signify?- a)The motion of a body with respect to other body
- b)Uniformly accelerated
- c)Non-uniformly accelerated
- d)Motion along a curve
Correct answer is option 'B'. Can you explain this answer?
What does relative motion signify?
a)
The motion of a body with respect to other body
b)
Uniformly accelerated
c)
Non-uniformly accelerated
d)
Motion along a curve
|
|
Joshua Pope answered |
Relative motion signifies the motion of a body with respect to another body. It is important to understand the concept of relative motion as it helps in analyzing the motion of objects in different reference frames.
- Definition:
Relative motion refers to the motion of an object in relation to another object. It involves comparing the motion of one object with respect to the motion of another object.
- Example:
For example, if a person is walking on a moving train, the person's motion is relative to the train. However, if we consider the motion of the person with respect to the ground, it would be different.
- Uniformly Accelerated Motion:
When a body moves with a constant acceleration, it is known as uniformly accelerated motion. In this type of motion, the velocity of the object changes by the same amount in equal intervals of time.
- Significance of Uniformly Accelerated Motion:
Understanding uniformly accelerated motion is essential in physics as many real-life scenarios involve objects that undergo acceleration. This type of motion helps in calculating various parameters like displacement, velocity, and acceleration of the object.
In conclusion, relative motion signifies the motion of a body with respect to another body, and understanding uniformly accelerated motion is crucial in analyzing the motion of objects in different reference frames.
- Definition:
Relative motion refers to the motion of an object in relation to another object. It involves comparing the motion of one object with respect to the motion of another object.
- Example:
For example, if a person is walking on a moving train, the person's motion is relative to the train. However, if we consider the motion of the person with respect to the ground, it would be different.
- Uniformly Accelerated Motion:
When a body moves with a constant acceleration, it is known as uniformly accelerated motion. In this type of motion, the velocity of the object changes by the same amount in equal intervals of time.
- Significance of Uniformly Accelerated Motion:
Understanding uniformly accelerated motion is essential in physics as many real-life scenarios involve objects that undergo acceleration. This type of motion helps in calculating various parameters like displacement, velocity, and acceleration of the object.
In conclusion, relative motion signifies the motion of a body with respect to another body, and understanding uniformly accelerated motion is crucial in analyzing the motion of objects in different reference frames.
Distance does not depend on _______- a)Initial point
- b)Final point
- c)Path taken
- d)Speed
Correct answer is option 'D'. Can you explain this answer?
Distance does not depend on _______
a)
Initial point
b)
Final point
c)
Path taken
d)
Speed
|
|
Orion Classes answered |
The distance depends on the final and initial points as these points define the path. Distance also depends on the path chosen, the distance between same initial and final point with different paths can be different. It does not depend on speed as whatever the speed may be, if the initial and final points and path remains same, the distance remains same.
Which of the following is the correct formula for average velocity?- a)v = dx/dt
- b)v = x/t
- c)v = xt
- d)v = t/x
Correct answer is option 'B'. Can you explain this answer?
Which of the following is the correct formula for average velocity?
a)
v = dx/dt
b)
v = x/t
c)
v = xt
d)
v = t/x
|
Benjamin Nelson answered |
Correct Formula for Average Velocity
Average velocity is defined as the displacement of an object divided by the time taken to cover that displacement. The correct formula for average velocity is:
v = Δx/Δt
Where:
- v represents the average velocity
- Δx represents the change in displacement
- Δt represents the change in time
Explanation
- When an object moves from one point to another, its displacement is given by the change in its position, which is represented by Δx.
- The time taken for the object to cover this displacement is represented by Δt.
- By dividing the change in displacement by the change in time, we get the average velocity of the object over that interval.
Therefore, the correct formula for average velocity is v = Δx/Δt, where Δx is the change in displacement and Δt is the change in time. This formula is essential in calculating the average speed of an object as it moves from one point to another over a specific time interval.
Average velocity is defined as the displacement of an object divided by the time taken to cover that displacement. The correct formula for average velocity is:
v = Δx/Δt
Where:
- v represents the average velocity
- Δx represents the change in displacement
- Δt represents the change in time
Explanation
- When an object moves from one point to another, its displacement is given by the change in its position, which is represented by Δx.
- The time taken for the object to cover this displacement is represented by Δt.
- By dividing the change in displacement by the change in time, we get the average velocity of the object over that interval.
Therefore, the correct formula for average velocity is v = Δx/Δt, where Δx is the change in displacement and Δt is the change in time. This formula is essential in calculating the average speed of an object as it moves from one point to another over a specific time interval.
In uniformly accelerated motion, how many variables are required to fully describe the system?- a)1
- b)3
- c)4
- d)2
Correct answer is option 'B'. Can you explain this answer?
In uniformly accelerated motion, how many variables are required to fully describe the system?
a)
1
b)
3
c)
4
d)
2
|
Daniel Walsh answered |
Understanding Uniformly Accelerated Motion
In uniformly accelerated motion, the system can be fully described using a set of variables. To understand why the correct answer is option 'B' (3 variables), let’s break down the components of the motion:
Key Variables in Uniformly Accelerated Motion
To fully characterize uniformly accelerated motion, you need the following three variables:
- Initial Velocity (u): This is the velocity of the object at the start of the observation period. It provides a baseline for how fast the object was moving before acceleration began.
- Acceleration (a): This represents the constant rate of change of velocity over time. It indicates how quickly the object's speed is increasing or decreasing.
- Time (t): This is the duration for which the object is in motion under the influence of acceleration. It helps in determining how long the acceleration affects the object.
Derived Variables
Once you have these three variables, you can calculate other important metrics, such as:
- Final Velocity (v): Using the equation v = u + at, you can determine how fast the object is moving after a certain time period.
- Displacement (s): The distance covered by the object during the acceleration can be calculated with the equation s = ut + (1/2)at².
Conclusion
In summary, three variables (initial velocity, acceleration, and time) are necessary to fully describe a system in uniformly accelerated motion. With these, you can derive other important parameters, but the basic three are essential for a complete understanding of the motion.
In uniformly accelerated motion, the system can be fully described using a set of variables. To understand why the correct answer is option 'B' (3 variables), let’s break down the components of the motion:
Key Variables in Uniformly Accelerated Motion
To fully characterize uniformly accelerated motion, you need the following three variables:
- Initial Velocity (u): This is the velocity of the object at the start of the observation period. It provides a baseline for how fast the object was moving before acceleration began.
- Acceleration (a): This represents the constant rate of change of velocity over time. It indicates how quickly the object's speed is increasing or decreasing.
- Time (t): This is the duration for which the object is in motion under the influence of acceleration. It helps in determining how long the acceleration affects the object.
Derived Variables
Once you have these three variables, you can calculate other important metrics, such as:
- Final Velocity (v): Using the equation v = u + at, you can determine how fast the object is moving after a certain time period.
- Displacement (s): The distance covered by the object during the acceleration can be calculated with the equation s = ut + (1/2)at².
Conclusion
In summary, three variables (initial velocity, acceleration, and time) are necessary to fully describe a system in uniformly accelerated motion. With these, you can derive other important parameters, but the basic three are essential for a complete understanding of the motion.
A body A is moving in North direction, while another body B is moving towards South. Velocity of A is greater than that of B. If North is taken as positive, which of the following relative velocities is positive?- a)Velocity of A with respect to B
- b)Velocity of B with respect to A
- c)Velocity of A with respect to ground
- d)Velocity of B with respect to ground
Correct answer is option 'A'. Can you explain this answer?
A body A is moving in North direction, while another body B is moving towards South. Velocity of A is greater than that of B. If North is taken as positive, which of the following relative velocities is positive?
a)
Velocity of A with respect to B
b)
Velocity of B with respect to A
c)
Velocity of A with respect to ground
d)
Velocity of B with respect to ground
|
|
Sebastian Diaz answered |
Explanation:
To analyze the relative velocities, we need to consider the velocities of the two bodies and the reference frame we are using.
Given information:
- Body A is moving in the North direction.
- Body B is moving in the South direction.
- Velocity of A is greater than that of B.
- North direction is taken as positive.
Relative velocities:
a) Velocity of A with respect to B:
- This refers to the velocity of A as observed from the point of view of B.
- Since A is moving in the North direction and B is moving in the opposite direction (South), the velocity of A with respect to B will be the sum of their individual velocities.
- In this case, A's velocity is positive (North) and B's velocity is negative (South).
- Therefore, the relative velocity of A with respect to B will be positive because the positive velocity of A exceeds the negative velocity of B.
b) Velocity of B with respect to A:
- This refers to the velocity of B as observed from the point of view of A.
- Since A is moving in the North direction and B is moving in the opposite direction (South), the velocity of B with respect to A will be the difference of their individual velocities.
- In this case, A's velocity is positive (North) and B's velocity is negative (South).
- Therefore, the relative velocity of B with respect to A will be negative because the negative velocity of B exceeds the positive velocity of A.
c) Velocity of A with respect to ground:
- This refers to the velocity of A as observed from the point of view of the ground, assuming that the ground is stationary.
- Since A is moving in the North direction and the ground is assumed to be stationary, the velocity of A with respect to the ground will be the same as its individual velocity, which is positive (North).
d) Velocity of B with respect to ground:
- This refers to the velocity of B as observed from the point of view of the ground, assuming that the ground is stationary.
- Since B is moving in the South direction and the ground is assumed to be stationary, the velocity of B with respect to the ground will be the same as its individual velocity, which is negative (South).
Therefore, the only relative velocity that is positive in this scenario is the velocity of A with respect to B.
To analyze the relative velocities, we need to consider the velocities of the two bodies and the reference frame we are using.
Given information:
- Body A is moving in the North direction.
- Body B is moving in the South direction.
- Velocity of A is greater than that of B.
- North direction is taken as positive.
Relative velocities:
a) Velocity of A with respect to B:
- This refers to the velocity of A as observed from the point of view of B.
- Since A is moving in the North direction and B is moving in the opposite direction (South), the velocity of A with respect to B will be the sum of their individual velocities.
- In this case, A's velocity is positive (North) and B's velocity is negative (South).
- Therefore, the relative velocity of A with respect to B will be positive because the positive velocity of A exceeds the negative velocity of B.
b) Velocity of B with respect to A:
- This refers to the velocity of B as observed from the point of view of A.
- Since A is moving in the North direction and B is moving in the opposite direction (South), the velocity of B with respect to A will be the difference of their individual velocities.
- In this case, A's velocity is positive (North) and B's velocity is negative (South).
- Therefore, the relative velocity of B with respect to A will be negative because the negative velocity of B exceeds the positive velocity of A.
c) Velocity of A with respect to ground:
- This refers to the velocity of A as observed from the point of view of the ground, assuming that the ground is stationary.
- Since A is moving in the North direction and the ground is assumed to be stationary, the velocity of A with respect to the ground will be the same as its individual velocity, which is positive (North).
d) Velocity of B with respect to ground:
- This refers to the velocity of B as observed from the point of view of the ground, assuming that the ground is stationary.
- Since B is moving in the South direction and the ground is assumed to be stationary, the velocity of B with respect to the ground will be the same as its individual velocity, which is negative (South).
Therefore, the only relative velocity that is positive in this scenario is the velocity of A with respect to B.
A ball is thrown up in the sky. After reaching a height, the ball falls back. What can be said about the average velocity?- a)It is non zero
- b)It is zero
- c)It is greater than zero
- d)It is less than zero
Correct answer is option 'B'. Can you explain this answer?
A ball is thrown up in the sky. After reaching a height, the ball falls back. What can be said about the average velocity?
a)
It is non zero
b)
It is zero
c)
It is greater than zero
d)
It is less than zero
|
Ethan Cooper answered |
Explanation:
When a ball is thrown up in the sky and then falls back down, its motion can be divided into two phases: the ascending phase and the descending phase. In the ascending phase, the ball moves in the opposite direction to the gravitational force, while in the descending phase, it moves in the same direction as the gravitational force.
Average Velocity Calculation:
To calculate the average velocity, we need to consider the total displacement and the total time taken. Displacement is the change in position of an object and can be calculated by subtracting the initial position from the final position.
In the case of the ball being thrown up and then falling back down, the total displacement is zero because the ball returns to its initial position. The total time taken is the sum of the time taken in the ascending phase and the time taken in the descending phase.
Ascending Phase:
During the ascending phase, the ball moves against the gravitational force. As the ball moves upwards, its velocity decreases until it reaches its maximum height, where its velocity becomes zero. Since the ball is moving in the opposite direction to the gravitational force, its average velocity during this phase is negative.
Descending Phase:
During the descending phase, the ball moves in the same direction as the gravitational force. Its velocity increases as it falls towards the ground. Again, the average velocity during this phase is negative because the ball is moving downwards.
Combining Phases:
Since the ball returns to its initial position, the total displacement is zero. The total time taken is the sum of the time taken in the ascending phase and the time taken in the descending phase. Since the average velocity is calculated by dividing the total displacement by the total time taken, and the total displacement is zero, the average velocity is zero.
Therefore, the correct answer is option 'b' - the average velocity is zero.
When a ball is thrown up in the sky and then falls back down, its motion can be divided into two phases: the ascending phase and the descending phase. In the ascending phase, the ball moves in the opposite direction to the gravitational force, while in the descending phase, it moves in the same direction as the gravitational force.
Average Velocity Calculation:
To calculate the average velocity, we need to consider the total displacement and the total time taken. Displacement is the change in position of an object and can be calculated by subtracting the initial position from the final position.
In the case of the ball being thrown up and then falling back down, the total displacement is zero because the ball returns to its initial position. The total time taken is the sum of the time taken in the ascending phase and the time taken in the descending phase.
Ascending Phase:
During the ascending phase, the ball moves against the gravitational force. As the ball moves upwards, its velocity decreases until it reaches its maximum height, where its velocity becomes zero. Since the ball is moving in the opposite direction to the gravitational force, its average velocity during this phase is negative.
Descending Phase:
During the descending phase, the ball moves in the same direction as the gravitational force. Its velocity increases as it falls towards the ground. Again, the average velocity during this phase is negative because the ball is moving downwards.
Combining Phases:
Since the ball returns to its initial position, the total displacement is zero. The total time taken is the sum of the time taken in the ascending phase and the time taken in the descending phase. Since the average velocity is calculated by dividing the total displacement by the total time taken, and the total displacement is zero, the average velocity is zero.
Therefore, the correct answer is option 'b' - the average velocity is zero.
A car is travelling in the north direction. To stop, it produces a deceleration of 60 m/s2. Which of the following is a correct representation for the deceleration?- a)60 m/s2 Northwards
- b)60 m/s2 Southwards
- c)60 m/s2 Eastwards
- d)60 m/s2 Westwards
Correct answer is option 'B'. Can you explain this answer?
A car is travelling in the north direction. To stop, it produces a deceleration of 60 m/s2. Which of the following is a correct representation for the deceleration?
a)
60 m/s2 Northwards
b)
60 m/s2 Southwards
c)
60 m/s2 Eastwards
d)
60 m/s2 Westwards
|
|
Orion Classes answered |
Deceleration always acts in the direction opposite to the direction of motion. Magnitude of deceleration is 60 m/s2 and it acts in the direction opposite to North. Hence the answer is 60 m/s2 Southwards.
The changes in displacement in three consecutive instances are 5 m, 4 m, 11 m, the total time taken is 5 s. What is the average velocity in m/s?- a)1
- b)4
- c)7
- d)6
Correct answer is option 'B'. Can you explain this answer?
The changes in displacement in three consecutive instances are 5 m, 4 m, 11 m, the total time taken is 5 s. What is the average velocity in m/s?
a)
1
b)
4
c)
7
d)
6
|
|
Ayesha Joshi answered |
The total change in displacement = 20 m. Total time taken = 5 s. Average velocity = total change in displacement/total time taken = 20/5 = 4 m/s.
A ball is thrown up in the sky, at what position will the instantaneous speed be minimum?- a)Initial position
- b)Final position
- c)Halfway through the whole trajectory
- d)After covering one fourth of the whole trajectory
Correct answer is option 'C'. Can you explain this answer?
A ball is thrown up in the sky, at what position will the instantaneous speed be minimum?
a)
Initial position
b)
Final position
c)
Halfway through the whole trajectory
d)
After covering one fourth of the whole trajectory
|
|
Orion Classes answered |
When the ball rises up, there will be a point where it will be in the state of instantaneous rest. At the this position the speed of the ball will be 0. Speed is maximum at the initial and final points.
A small block is placed over another block which is moving with a velocity of 5m/s. What is the absolute velocity of the small block?- a)5m/s
- b)10m/s
- c)0m/s
- d)14m/s
Correct answer is option 'A'. Can you explain this answer?
A small block is placed over another block which is moving with a velocity of 5m/s. What is the absolute velocity of the small block?
a)
5m/s
b)
10m/s
c)
0m/s
d)
14m/s
|
Nora Barnes answered |
Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. In this scenario, we have a small block placed over another block that is already moving with a velocity of 5m/s. We are required to find the absolute velocity of the small block.
Absolute Velocity: The absolute velocity of an object is the velocity of the object with respect to a fixed reference point or frame of reference. In other words, it is the velocity of the object relative to an observer who is stationary or not moving.
To determine the absolute velocity of the small block, we need to consider the velocity of the small block with respect to the stationary observer. Since the small block is placed on top of the moving block, it will have the same velocity as the moving block.
Therefore, the absolute velocity of the small block is equal to the velocity of the moving block, which is given as 5m/s.
Hence, the correct answer is option 'A' - 5m/s.
Absolute Velocity: The absolute velocity of an object is the velocity of the object with respect to a fixed reference point or frame of reference. In other words, it is the velocity of the object relative to an observer who is stationary or not moving.
To determine the absolute velocity of the small block, we need to consider the velocity of the small block with respect to the stationary observer. Since the small block is placed on top of the moving block, it will have the same velocity as the moving block.
Therefore, the absolute velocity of the small block is equal to the velocity of the moving block, which is given as 5m/s.
Hence, the correct answer is option 'A' - 5m/s.
Select the CORRECT option from the following.- a)Weight is the vector quantity and mass is scalar quantity
- b)Mass and weight are scalar quantities
- c)Mass is the vector quantity and weight is the scalar quantity
- d)Weight and mass are vector quantities
Correct answer is option 'A'. Can you explain this answer?
Select the CORRECT option from the following.
a)
Weight is the vector quantity and mass is scalar quantity
b)
Mass and weight are scalar quantities
c)
Mass is the vector quantity and weight is the scalar quantity
d)
Weight and mass are vector quantities
|
Flembe Academy answered |
All physical quantities are classified into two types:
Scalar Quantity:
- A physical quantity having magnitude only is called scalar quantity. They have numerical value only and these quantities do not specify the direction
- Example: Length, Time, Speed, Mass, Density, Pressure, Temperature, Energy, Work, Power
Vector quantity:
- A physical quantity having both magnitude and direction is called vector quantities. It is represented by a straight line with an arrowhead
- Example: Displacement, Velocity, Acceleration, Force, Momentum, Weight
Which one of the following operations is valid?- a)Vector multiplied by scalar
- b)Vector added to scalar
- c)Vector subtracted from scalar
- d)Vector divided by vector
Correct answer is option 'A'. Can you explain this answer?
Which one of the following operations is valid?
a)
Vector multiplied by scalar
b)
Vector added to scalar
c)
Vector subtracted from scalar
d)
Vector divided by vector
|
|
Flembe Academy answered |
Only operations valid for vector with scalars are multiplication and division. A vector can be multiplied or divided by a scalar. Other operations like addition and subtraction are not valid for vectors with scalars.
The operation used to obtain a scalar from two vectors is ______- a)Cross product
- b)Dot product
- c)Simple product
- d)Complex product
Correct answer is option 'B'. Can you explain this answer?
The operation used to obtain a scalar from two vectors is ______
a)
Cross product
b)
Dot product
c)
Simple product
d)
Complex product
|
Isabella Iqbal answered |
Understanding Scalar Operations from Vectors
When dealing with vectors, there are specific operations that can yield different types of results. One such operation that produces a scalar is the Dot Product.
What is the Dot Product?
- The dot product, also known as the scalar product, is an operation that takes two vectors and returns a single scalar value.
- Mathematically, if you have two vectors A and B, the dot product is calculated as:
- A · B = |A| |B| cos(θ)
- Here, |A| and |B| are the magnitudes of the vectors, and θ is the angle between them.
Properties of the Dot Product
- Commutative: A · B = B · A
- Distributive: A · (B + C) = A · B + A · C
- Associative with Scalars: k(A · B) = (kA) · B = A · (kB)
Applications of the Dot Product
- The dot product is crucial in various applications, including:
- Determining the angle between two vectors.
- Assessing the projection of one vector onto another.
- Calculating work done when a force is applied along a displacement.
Conclusion
In summary, the operation used to obtain a scalar from two vectors is the Dot Product. It serves as a fundamental tool in vector mathematics, enabling calculations that are pivotal in physics and engineering. Understanding this operation is essential for solving various problems involving vectors.
When dealing with vectors, there are specific operations that can yield different types of results. One such operation that produces a scalar is the Dot Product.
What is the Dot Product?
- The dot product, also known as the scalar product, is an operation that takes two vectors and returns a single scalar value.
- Mathematically, if you have two vectors A and B, the dot product is calculated as:
- A · B = |A| |B| cos(θ)
- Here, |A| and |B| are the magnitudes of the vectors, and θ is the angle between them.
Properties of the Dot Product
- Commutative: A · B = B · A
- Distributive: A · (B + C) = A · B + A · C
- Associative with Scalars: k(A · B) = (kA) · B = A · (kB)
Applications of the Dot Product
- The dot product is crucial in various applications, including:
- Determining the angle between two vectors.
- Assessing the projection of one vector onto another.
- Calculating work done when a force is applied along a displacement.
Conclusion
In summary, the operation used to obtain a scalar from two vectors is the Dot Product. It serves as a fundamental tool in vector mathematics, enabling calculations that are pivotal in physics and engineering. Understanding this operation is essential for solving various problems involving vectors.
A caterpillar starts travelling at a speed of 1 m/h. If the rate at which the speed changes is 0.1 m/h2, what is the final speed after 10 Hrs?- a)2 m/h
- b)1 m/h
- c)0.5 m/h
- d)5 m/h
Correct answer is option 'A'. Can you explain this answer?
A caterpillar starts travelling at a speed of 1 m/h. If the rate at which the speed changes is 0.1 m/h2, what is the final speed after 10 Hrs?
a)
2 m/h
b)
1 m/h
c)
0.5 m/h
d)
5 m/h
|
|
Eliana White answered |
Given:
Initial speed (u) = 1 m/h
Rate of change of speed (a) = 0.1 m/h²
Time (t) = 10 hrs
To find:
Final speed (v) after 10 hrs.
Formula:
The formula to calculate final speed is:
v = u + at
Calculation:
Substituting the given values into the formula, we get:
v = 1 + 0.1 * 10
v = 1 + 1
v = 2 m/h
Therefore, the final speed after 10 hrs is 2 m/h.
Explanation:
- The initial speed of the caterpillar is given as 1 m/h.
- The rate at which the speed changes is given as 0.1 m/h². This means that for every hour, the speed of the caterpillar increases by 0.1 m/h.
- The time is given as 10 hrs.
- Using the formula v = u + at, we can calculate the final speed.
- Substituting the given values into the formula, we find that the final speed is 2 m/h.
- This means that after 10 hrs, the caterpillar will be traveling at a speed of 2 m/h.
Initial speed (u) = 1 m/h
Rate of change of speed (a) = 0.1 m/h²
Time (t) = 10 hrs
To find:
Final speed (v) after 10 hrs.
Formula:
The formula to calculate final speed is:
v = u + at
Calculation:
Substituting the given values into the formula, we get:
v = 1 + 0.1 * 10
v = 1 + 1
v = 2 m/h
Therefore, the final speed after 10 hrs is 2 m/h.
Explanation:
- The initial speed of the caterpillar is given as 1 m/h.
- The rate at which the speed changes is given as 0.1 m/h². This means that for every hour, the speed of the caterpillar increases by 0.1 m/h.
- The time is given as 10 hrs.
- Using the formula v = u + at, we can calculate the final speed.
- Substituting the given values into the formula, we find that the final speed is 2 m/h.
- This means that after 10 hrs, the caterpillar will be traveling at a speed of 2 m/h.
When person moves in the coordinate system from A (0, 0) to B (5, 10), to C (8, 6), what is the displacement covered?- a)10 units
- b)5 units
- c)7 units
- d)15 units
Correct answer is option 'A'. Can you explain this answer?
When person moves in the coordinate system from A (0, 0) to B (5, 10), to C (8, 6), what is the displacement covered?
a)
10 units
b)
5 units
c)
7 units
d)
15 units
|
|
Orion Classes answered |
The displacement is the distance between the final and the initial location. Here the final location is C and the initial is A. We can solve this by using distance between two points method. AC = Square root ((82 – 02) + (62 – 02)) = Square root (100) = 10 units.
A bus moves the first few meters of its journey with an acceleration of 5 m/s2 in 10s and the next few meters with an acceleration of 15 m/s2 in 20s. What is the final velocity in m/s if it starts from rest?- a)100
- b)350
- c)450
- d)400
Correct answer is option 'B'. Can you explain this answer?
A bus moves the first few meters of its journey with an acceleration of 5 m/s2 in 10s and the next few meters with an acceleration of 15 m/s2 in 20s. What is the final velocity in m/s if it starts from rest?
a)
100
b)
350
c)
450
d)
400
|
|
Orion Classes answered |
Apply the first equation of motion in both the parts. For first part, v1 = u + a1t1 = 0 + 5×10 = 50 m/s. For second part, v2 = u2 (= v1) + a2t2 = 50 + 15×20 = 350 m/s.
A uniformly accelerated body has ____- a)Constant speed
- b)Constant velocity
- c)Constant force
- d)Constant momentum
Correct answer is option 'C'. Can you explain this answer?
A uniformly accelerated body has ____
a)
Constant speed
b)
Constant velocity
c)
Constant force
d)
Constant momentum
|
|
Orion Classes answered |
Since the body is accelerated, the speed and velocity will vary. Momentum depends on velocity; hence the momentum will also vary. The force remains constant as F = ma.
An observer is sitting on a car moving with some constant velocity. The observer sees things around him, in the ____- a)Relative frame of reference
- b)Absolute frame of reference
- c)Valid frame of reference
- d)Ground frame of reference
Correct answer is option 'A'. Can you explain this answer?
An observer is sitting on a car moving with some constant velocity. The observer sees things around him, in the ____
a)
Relative frame of reference
b)
Absolute frame of reference
c)
Valid frame of reference
d)
Ground frame of reference
|
|
Orion Classes answered |
The observer is not stationary with respect to ground. The observer is stationary with respect to the frame of the moving car, i.e., to the relative frame of reference. The observer will see everything around him/her with respect to the relative frame of reference.
A point is moving with uniform acceleration, in the eleventh and fifteenth seconds from the commencement it moves through 640 and 840 cms respectively, find its initial velocity, and the acceleration with which it moves?- a)135 cm/s, 60 cm/s2
- b)100 cm/s, 45 cm/s2
- c)90 cm/s, 60 cm/s2
- d)115 cm/s, 50 cm/s2
Correct answer is option 'D'. Can you explain this answer?
A point is moving with uniform acceleration, in the eleventh and fifteenth seconds from the commencement it moves through 640 and 840 cms respectively, find its initial velocity, and the acceleration with which it moves?
a)
135 cm/s, 60 cm/s2
b)
100 cm/s, 45 cm/s2
c)
90 cm/s, 60 cm/s2
d)
115 cm/s, 50 cm/s2
|
|
Daniel Walsh answered |
Given data:
- Initial velocity (u) = ?
- Final velocity in the 11th second = 640 cm/s
- Final velocity in the 15th second = 840 cm/s
- Time taken to reach the final velocity in the 11th second = 11 seconds
- Time taken to reach the final velocity in the 15th second = 15 seconds
- Acceleration (a) = ?
Calculating initial velocity:
1. Using the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
2. For the 11th second: 640 = u + 11a
3. For the 15th second: 840 = u + 15a
4. Subtracting the two equations: 840 - 640 = 15a - 11a
5. 200 = 4a
6. Therefore, a = 50 cm/s2
7. Substituting the value of a in the equation for the 11th second: 640 = u + 11(50)
8. Solving for u, we get u = 115 cm/s
Therefore, the initial velocity is 115 cm/s and the acceleration is 50 cm/s2.
- Initial velocity (u) = ?
- Final velocity in the 11th second = 640 cm/s
- Final velocity in the 15th second = 840 cm/s
- Time taken to reach the final velocity in the 11th second = 11 seconds
- Time taken to reach the final velocity in the 15th second = 15 seconds
- Acceleration (a) = ?
Calculating initial velocity:
1. Using the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
2. For the 11th second: 640 = u + 11a
3. For the 15th second: 840 = u + 15a
4. Subtracting the two equations: 840 - 640 = 15a - 11a
5. 200 = 4a
6. Therefore, a = 50 cm/s2
7. Substituting the value of a in the equation for the 11th second: 640 = u + 11(50)
8. Solving for u, we get u = 115 cm/s
Therefore, the initial velocity is 115 cm/s and the acceleration is 50 cm/s2.
The expression for displacement is x = sin(5t). The expression for acceleration is ______- a)5sin(5t)
- b)25cos(5t)
- c)-25sin(5t)
- d)-5cost(5t)
Correct answer is option 'A'. Can you explain this answer?
The expression for displacement is x = sin(5t). The expression for acceleration is ______
a)
5sin(5t)
b)
25cos(5t)
c)
-25sin(5t)
d)
-5cost(5t)
|
|
Orion Classes answered |
Acceleration = dv/dt = d2x/dt2. The velocity (v) can be expressed as, v = dx/dt = 5cos(5t). Hence acceleration (a) becomes, a = dv/dt = -25sin(5t).
In which coordinate system do we use distance from origin and to angles to define the position of a point in space?- a)Cartesian
- b)Cylindrical
- c)Spherical
- d)2-D Cartesian
Correct answer is option 'C'. Can you explain this answer?
In which coordinate system do we use distance from origin and to angles to define the position of a point in space?
a)
Cartesian
b)
Cylindrical
c)
Spherical
d)
2-D Cartesian
|
|
Orion Classes answered |
In Spherical system, distance from the center, the angle with the X axis, and the angle with the Z axis are used to define the position of a point. These are respectively represented by R, θ and ф.
What is the path length of the following path?
A (0, 0) to B (5, 0) to C (5, 5) to D (0, 5)- a)20 units
- b)25 units
- c)15 units
- d)10 units
Correct answer is option 'C'. Can you explain this answer?
What is the path length of the following path?
A (0, 0) to B (5, 0) to C (5, 5) to D (0, 5)
A (0, 0) to B (5, 0) to C (5, 5) to D (0, 5)
a)
20 units
b)
25 units
c)
15 units
d)
10 units
|
|
Elijah Hines answered |
Path Length Calculation:
To calculate the path length of the given path from point A to point D passing through points B and C, we can use the distance formula to find the distance between each pair of consecutive points.
Distance between A and B:
Using the distance formula,
Distance between A(0, 0) and B(5, 0) = √((5-0)^2 + (0-0)^2)
= √(5^2 + 0^2)
= √25
= 5 units
Distance between B and C:
Distance between B(5, 0) and C(5, 5) = √((5-5)^2 + (5-0)^2)
= √(0^2 + 5^2)
= √25
= 5 units
Distance between C and D:
Distance between C(5, 5) and D(0, 5) = √((0-5)^2 + (5-5)^2)
= √((-5)^2 + 0^2)
= √25
= 5 units
Total Path Length:
Adding the distances of each segment:
5 units + 5 units + 5 units = 15 units
Therefore, the path length of the given path from point A to point D passing through points B and C is 15 units. Hence, the correct answer is option 'c'.
To calculate the path length of the given path from point A to point D passing through points B and C, we can use the distance formula to find the distance between each pair of consecutive points.
Distance between A and B:
Using the distance formula,
Distance between A(0, 0) and B(5, 0) = √((5-0)^2 + (0-0)^2)
= √(5^2 + 0^2)
= √25
= 5 units
Distance between B and C:
Distance between B(5, 0) and C(5, 5) = √((5-5)^2 + (5-0)^2)
= √(0^2 + 5^2)
= √25
= 5 units
Distance between C and D:
Distance between C(5, 5) and D(0, 5) = √((0-5)^2 + (5-5)^2)
= √((-5)^2 + 0^2)
= √25
= 5 units
Total Path Length:
Adding the distances of each segment:
5 units + 5 units + 5 units = 15 units
Therefore, the path length of the given path from point A to point D passing through points B and C is 15 units. Hence, the correct answer is option 'c'.
The relative velocity of a body A with respect to a body B is 5 m/s. The absolute velocity of body B is 10 m/s. Both the bodies are moving in the same direction. What is the absolute velocity of body A?- a)10m/s
- b)15m/s
- c)-5m/s
- d)0m/s
Correct answer is option 'B'. Can you explain this answer?
The relative velocity of a body A with respect to a body B is 5 m/s. The absolute velocity of body B is 10 m/s. Both the bodies are moving in the same direction. What is the absolute velocity of body A?
a)
10m/s
b)
15m/s
c)
-5m/s
d)
0m/s
|
|
Elijah Hines answered |
Relative and Absolute Velocity
- Relative velocity of body A with respect to body B = 5 m/s
- Absolute velocity of body B = 10 m/s
- Both bodies are moving in the same direction
Finding Absolute Velocity of Body A
- When two bodies are moving in the same direction, the absolute velocity of one body with respect to the other can be found by adding the relative velocity to the absolute velocity of the other body.
- Absolute velocity of body A = Absolute velocity of body B + Relative velocity of A with respect to B
- Absolute velocity of body A = 10 m/s + 5 m/s
- Absolute velocity of body A = 15 m/s
Therefore, the absolute velocity of body A is 15 m/s. So, the correct answer is option 'B' 15 m/s.
- Relative velocity of body A with respect to body B = 5 m/s
- Absolute velocity of body B = 10 m/s
- Both bodies are moving in the same direction
Finding Absolute Velocity of Body A
- When two bodies are moving in the same direction, the absolute velocity of one body with respect to the other can be found by adding the relative velocity to the absolute velocity of the other body.
- Absolute velocity of body A = Absolute velocity of body B + Relative velocity of A with respect to B
- Absolute velocity of body A = 10 m/s + 5 m/s
- Absolute velocity of body A = 15 m/s
Therefore, the absolute velocity of body A is 15 m/s. So, the correct answer is option 'B' 15 m/s.
What is a scalar?- a)A quantity with only magnitude
- b)A quantity with only direction
- c)A quantity with both magnitude and direction
- d)A quantity without magnitude
Correct answer is option 'A'. Can you explain this answer?
What is a scalar?
a)
A quantity with only magnitude
b)
A quantity with only direction
c)
A quantity with both magnitude and direction
d)
A quantity without magnitude
|
|
Flembe Academy answered |
A scalar quantity is one which only has a magnitude. Examples of scalar quantities are mass, volume, work, energy etc.
Which of the following types of motion can be used for describing the motion of a car on a straight road?- a)Rectilinear
- b)Circular
- c)Periodic
- d)Harmonic
Correct answer is option 'A'. Can you explain this answer?
Which of the following types of motion can be used for describing the motion of a car on a straight road?
a)
Rectilinear
b)
Circular
c)
Periodic
d)
Harmonic
|
|
Orion Classes answered |
The motion of a car on straight road is happening along a straight line. Hence the motion can be called rectilinear as rectilinear motion happens along a straight line. Rest all are non rectilinear motions.
Which of the following measures as vector quantity?- a)40°
- b)10-19 coulomb
- c)20 m/s2
- d)10 kg
Correct answer is option 'C'. Can you explain this answer?
Which of the following measures as vector quantity?
a)
40°
b)
10-19 coulomb
c)
20 m/s2
d)
10 kg
|
|
Flembe Academy answered |
Concept:
- Vector Quantity: Physical quantities that have magnitude and direction and obey triangle law are called vector quantities.
- Example: Displacement, Velocity, etc.
Additional Information
- The velocity of a moving object is defined as the displacement of the object in the unit time interval.
- It is a vector quantity and its SI unit is meter/second.
- Acceleration of an object is defined as the rate of change of velocity of the object.
- It is a vector quantity and its SI unit is (m/s2)
- ∴ The correct answer is 20 m/s2.
A coin and a bag full of rocks are thrown in a gravity less environment with the same initial speed. Which one of the following statements is true about the situation?- a)The bag will travel faster
- b)The coin will travel faster
- c)Both will travel with the same speed
- d)Bag will not move
Correct answer is option 'C'. Can you explain this answer?
A coin and a bag full of rocks are thrown in a gravity less environment with the same initial speed. Which one of the following statements is true about the situation?
a)
The bag will travel faster
b)
The coin will travel faster
c)
Both will travel with the same speed
d)
Bag will not move
|
|
Scarlett Coleman answered |
Explanation:
Initial Speed:
- In a gravity-less environment, both the coin and the bag of rocks will have the same initial speed when thrown.
Effect of Gravity:
- In a gravity-less environment, there is no force acting on the objects to change their speed or direction.
- Therefore, both the coin and the bag of rocks will continue to move at the same speed without any acceleration or deceleration.
Newton's First Law of Motion:
- According to Newton's First Law of Motion, an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an external force.
- Since there are no external forces acting on the coin or the bag of rocks in this scenario, they will continue to move with the same speed.
Conclusion:
- Therefore, both the coin and the bag of rocks will travel with the same speed in a gravity-less environment.
In the first 10s of a body’s motion, the velocity changes from 10 m/s to 20m/s. During the next 30s the velocity changes from 20m/s to 50m/s. What is the average acceleration in m/s2?- a)1
- b)2
- c)3
- d)0.5
Correct answer is option 'A'. Can you explain this answer?
In the first 10s of a body’s motion, the velocity changes from 10 m/s to 20m/s. During the next 30s the velocity changes from 20m/s to 50m/s. What is the average acceleration in m/s2?
a)
1
b)
2
c)
3
d)
0.5
|
|
Orion Classes answered |
Average acceleration is the total change in velocity by the total change in time. Here, total change in velocity = 50 - 10 = 40m/s, and total change in time = 30 + 10 = 40s. Therefore, average acceleration = 1 m/s2.
A truck is moving with 40 m/s velocity, a train is moving with a velocity of 80 m/s. How fast is the rain moving with respect to the truck?- a)40 m/s faster
- b)-40 m/s faster
- c)40 m/s slower
- d)60 m/s slower
Correct answer is option 'A'. Can you explain this answer?
A truck is moving with 40 m/s velocity, a train is moving with a velocity of 80 m/s. How fast is the rain moving with respect to the truck?
a)
40 m/s faster
b)
-40 m/s faster
c)
40 m/s slower
d)
60 m/s slower
|
|
Josephine Myers answered |
Relative Velocity Calculation:
In order to determine how fast the rain is moving with respect to the truck, we need to calculate the relative velocity between the rain and the truck.
Relative Velocity Formula:
The relative velocity between two objects moving in the same direction is calculated by subtracting the velocity of the slower object from the velocity of the faster object.
Given Information:
Truck velocity = 40 m/s
Train velocity = 80 m/s
Calculation:
Relative velocity = Train velocity - Truck velocity
Relative velocity = 80 m/s - 40 m/s
Relative velocity = 40 m/s
Therefore, the rain is moving 40 m/s faster with respect to the truck. Hence, the correct answer is option 'A'.
In order to determine how fast the rain is moving with respect to the truck, we need to calculate the relative velocity between the rain and the truck.
Relative Velocity Formula:
The relative velocity between two objects moving in the same direction is calculated by subtracting the velocity of the slower object from the velocity of the faster object.
Given Information:
Truck velocity = 40 m/s
Train velocity = 80 m/s
Calculation:
Relative velocity = Train velocity - Truck velocity
Relative velocity = 80 m/s - 40 m/s
Relative velocity = 40 m/s
Therefore, the rain is moving 40 m/s faster with respect to the truck. Hence, the correct answer is option 'A'.
Chapter doubts & questions for Motion in a straight line - Science for ACT 2025 is part of ACT exam preparation. The chapters have been prepared according to the ACT exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for ACT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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