Motion - Practice Test, Science, Class 9 - Class 9 MCQ

15 m/s

[Hint: 54×1000m/3600s = 15m/s]

Scalar Quantity

A scalar quantity is a type of physical quantity that has magnitude only and does not have any specific direction associated with it. It can be represented by a single real number or value.

Characteristics of Scalar Quantities

• Magnitude: Scalar quantities only have magnitude, which refers to the size or amount of the quantity. It is represented by a numerical value and a unit.

Examples of Scalar Quantities

• Mass


• Temperature


• Time


• Distance


• Speed


• Energy


• Pressure


• Volume

In these examples, the scalar quantities are described by their magnitude alone, without any specific direction. For example, the mass of an object is simply stated as a numerical value (e.g., 2 kg) without indicating any direction.

Therefore, the correct answer is A: magnitude only.

Explanation:
When an object undergoes acceleration, several things happen:
1. Change in Velocity:
Acceleration is defined as the rate of change of velocity. Therefore, when an object undergoes acceleration, there is a change in its velocity. This change can be in magnitude, direction, or both.
2. Increase in Speed:
Speed is the magnitude of velocity. If the object is accelerating, it means there is a change in its velocity, which implies that its speed is increasing.
3. Force:
Acceleration is caused by a force acting on an object. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, when an object undergoes acceleration, there must be a force acting on it.
Summary:
- When an object undergoes acceleration, there is a change in its velocity.
- This change can be in magnitude, direction, or both, leading to an increase in speed.
- Acceleration is caused by a force acting on the object.
Therefore, the correct answer is option C: a force always acting on it.

To determine the SI unit of retardation, we need to understand what retardation represents. Retardation is the rate at which an object's velocity decreases. It is also known as deceleration.
The SI unit for velocity is meters per second (m/s), and the SI unit for time is seconds (s). Since retardation represents the change in velocity per unit time, the SI unit for retardation can be obtained by dividing the SI unit for velocity by the SI unit for time.
Therefore, the SI unit of retardation is m/s divided by s, which simplifies to m/s².
Hence, the correct answer is option B: ms^-2.

To find the average speed of the car for the round trip, we need to calculate the total distance traveled and divide it by the total time taken.
Step 1: Calculate the distance traveled from city A to city B and back to city A.
- The car travels 50 km from city A to city B.
- The car then travels an additional 50 km from city B back to city A.
- Therefore, the total distance traveled is 50 km + 50 km = 100 km.
Step 2: Calculate the total time taken for the round trip.
- It took 2 hours for the round trip.
Step 3: Calculate the average speed.
- Average speed = total distance / total time
- Average speed = 100 km / 2 hours
- Average speed = 50 km/h
Therefore, the average speed of the car for this round trip is 50 km/h, which corresponds to option C.

Explanation:
The equation v = u + at describes the relationship between velocity (v), initial velocity (u), acceleration (a), and time (t).
- Velocity is a function of time: The equation v = u + at shows that velocity (v) is dependent on time (t). As time increases, the velocity also changes accordingly.
- Velocity is not a function of position: The equation v = u + at does not involve any information regarding position. It only relates velocity to initial velocity, acceleration, and time.
- Position is not a function of time: The equation v = u + at does not provide any information about the position of an object. It solely deals with the velocity of the object.
- Position is not a function of velocity and time: The equation v = u + at does not include any terms related to position. It only describes the relationship between velocity, initial velocity, acceleration, and time.
Therefore, the correct answer is A: Velocity is a function of time.

Explanation:
To determine the acceleration of a moving object, we can use the slope of the velocity-time graph. Here's how:
1. Velocity-Time Graph: The velocity-time graph represents the change in velocity of an object over time. The slope of this graph represents acceleration.
2. Slope of Velocity-Time Graph: The slope of the velocity-time graph can be calculated by dividing the change in velocity by the change in time. This gives us the rate at which the velocity is changing, which is the definition of acceleration.
3. Acceleration: Acceleration is the rate at which an object changes its velocity. It can be positive (when the object is speeding up) or negative (when the object is slowing down).
4. Area of Velocity-Time Graph: The area under the velocity-time graph represents the displacement of the object. It does not directly provide information about acceleration.
5. Distance-Time Graph: The distance-time graph represents the change in distance of an object over time. The slope of this graph represents the object's speed, not acceleration.
Therefore, the correct answer is B: slope of the velocity-time graph. The slope of the velocity-time graph can determine the acceleration of a moving object.

Explanation:
To solve this problem, we need to analyze the motion of the body using the given information.
1. The body is projected up with an initial velocity u m/s.
2. It goes up to a height h meters in t seconds time.
3. Then it comes back to the point of projection.
Now, let's analyze each statement and determine if it is true or false.
Statement A: The acceleration is zero.
- False. The body is under the influence of gravity, so it experiences a constant acceleration of -9.8 m/s^2 (assuming no other forces act on it).
Statement B: The displacement is zero.
- True. The body starts and ends at the same point of projection, so the displacement is zero.
Statement C: The average velocity is 2h/t.
- False. The average velocity can be calculated as the total displacement divided by the total time taken. In this case, since the displacement is zero, the average velocity is also zero.
Statement D: The final velocity is 2u when the body reaches the projection point.
- False. The final velocity of the body when it reaches the projection point is equal to its initial velocity. Therefore, the final velocity is simply u, not 2u.
Therefore, the correct answer is Statement B: The displacement is zero.

To find the increase in velocity, we can use the formula:
Δv = a * t
Where:
- Δv is the change in velocity
- a is the acceleration
- t is the time
Given:
- Acceleration (a) = 1.5 m/s^2
- Time (t) = 4s
Substituting the given values into the formula, we have:
Δv = 1.5 m/s^2 * 4s
= 6 m/s
Therefore, the increase in velocity in 4 seconds is 6 m/s.
Answer: A. 6 m/s

Explanation:
To determine the correct statement, we need to understand the differences between speed and velocity.
Speed:
- Speed is a scalar quantity, which means it only has a magnitude and no direction.
- It is defined as the distance traveled per unit of time.
- The formula for speed is: speed = distance / time.
- The SI unit for speed is meters per second (m/s).
Velocity:
- Velocity is a vector quantity, which means it has both magnitude and direction.
- It is defined as the displacement traveled per unit of time.
- The formula for velocity is: velocity = displacement / time.
- The SI unit for velocity is also meters per second (m/s).
Comparison:
Based on the definitions and characteristics of speed and velocity, we can determine the correct statement:
- Option A is incorrect because speed and velocity are not the same. Speed is a scalar, while velocity is a vector.
- Option B is correct. Speed is a scalar quantity, while velocity is a vector quantity.
- Option C is incorrect because speed is not a vector, and velocity is not a scalar.
- Option D is incorrect because option B is correct.
Therefore, the correct statement is B: speed is a scalar and velocity is a vector.

The slope of the body when it moves with uniform velocity is zero.

When a body moves with uniform velocity, it means that it is moving in a straight line with a constant speed. In this case, the body's position-time graph will be a straight line with a constant slope, which represents the velocity of the body.

The slope of a straight line is defined as the change in the y-coordinate divided by the change in the x-coordinate. In the case of a position-time graph, the y-coordinate represents the position of the body and the x-coordinate represents time.

Since the body is moving with uniform velocity, the change in position (y-coordinate) will be constant for any given change in time (x-coordinate). This means that the slope of the position-time graph will always be constant and equal to the velocity of the body.

However, since the body is moving with a constant velocity, there is no change in position over time. This means that the change in the y-coordinate is zero for any given change in the x-coordinate. Therefore, the slope of the position-time graph is zero.

In conclusion, when a body moves with uniform velocity, the slope of its position-time graph is zero.

Area of Velocity-Time Graph
The area under a velocity-time graph represents the displacement of an object. The velocity-time graph is a graphical representation of an object's velocity over a specific time period. The area under the curve of this graph can provide valuable information about the object's displacement during that time.
Explanation:
To understand why the area under the velocity-time graph represents displacement, we need to consider the relationship between velocity and displacement. Velocity is defined as the rate of change of displacement with respect to time. In other words, velocity tells us how the displacement of an object changes over time.
When we have a constant velocity, the displacement of an object is simply the product of its velocity and the time it traveled. This can be represented by a rectangle on the velocity-time graph, where the height of the rectangle corresponds to the constant velocity and the width corresponds to the time interval.
However, when the velocity is not constant, the displacement cannot be determined using a simple rectangle. Instead, we need to consider the different segments of the velocity-time graph and calculate the area under each segment separately.
By calculating the area under each segment of the velocity-time graph and summing them up, we can determine the total displacement of the object during the given time period.
Therefore, the area of the velocity-time graph gives us the displacement of an object, making the correct answer to the question C: displacement.

The slope of a velocity-time graph gives the acceleration of an object.
Explanation:
- The velocity-time graph represents the relationship between velocity and time for an object.
- The slope of this graph at any point represents the rate of change of velocity with respect to time, which is the definition of acceleration.
- The slope can be calculated by dividing the change in velocity by the change in time between two points on the graph.
- If the slope is positive, it indicates that the velocity is increasing, which means the object is accelerating in the positive direction.
- If the slope is negative, it indicates that the velocity is decreasing, which means the object is decelerating or accelerating in the negative direction.
- The magnitude of the slope represents the magnitude of acceleration. A steeper slope indicates a higher acceleration, while a flatter slope indicates a lower acceleration.
- Therefore, the slope of a velocity-time graph gives the acceleration of an object.
Conclusion:
The slope of a velocity-time graph gives the acceleration of an object.

Explanation:
A vector gives both direction and magnitude. Here's a breakdown of the explanation:
Direction:
- A vector represents a specific direction in space.
- It indicates the orientation or heading of an object or quantity.
- For example, the direction of a velocity vector represents the direction of motion.
Magnitude:
- The magnitude of a vector represents the size or length of the vector.
- It provides information about the quantity or intensity of the vector.
- For example, the magnitude of a velocity vector represents the speed of an object.
Scalar:
- A scalar only has magnitude and does not have direction.
- Scalars are quantities that can be completely described by their magnitude alone.
- Examples of scalars include temperature, mass, and time.
Conclusion:
- The option B: vector is the correct answer as it gives both direction and magnitude.
- Scalars (option A) only have magnitude, while option C (both) is incorrect.
- Option D (none) is also incorrect as vectors indeed have both direction and magnitude.

When a moving body comes to rest, its acceleration is negative. Let's understand why:
1. Acceleration: Acceleration is the rate of change of velocity with respect to time. It is a vector quantity and can be positive, negative, or zero.
2. Rest: When a body comes to rest, it means that its velocity becomes zero. This implies that there is no change in velocity over time.
3. Change in velocity: Since the velocity becomes zero, the change in velocity is negative. This is because the initial velocity is in one direction (forward) and the final velocity is in the opposite direction (backward).
4. Acceleration and change in velocity: As acceleration is the rate of change of velocity, a negative change in velocity indicates a negative acceleration.
5. Conclusion: Therefore, when a moving body comes to rest, its acceleration is negative. So, option C is the correct answer.
Note: The acceleration can also be zero if the initial velocity is zero and the body remains at rest. However, in this question, it is mentioned that the body comes to rest, which means it had an initial velocity. Hence, the acceleration is negative.

The Acceleration of a Body Starting from Rest
When a body starts from rest, it means that initially, the body is not moving and its velocity is zero. In this scenario, we can determine the characteristics of the body's acceleration.
1. Definition of Acceleration:
Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, meaning it has both magnitude and direction.
2. Acceleration of a Body Starting from Rest:
When a body starts from rest, its initial velocity is zero. Therefore, the change in velocity (∆v) is equal to the final velocity (vf) minus zero, which simplifies to ∆v = vf - 0 = vf.
3. Types of Acceleration:
There are different types of acceleration that a body can experience. In the case of a body starting from rest, the following types of acceleration can be observed:
- Positive Acceleration: If the body's velocity increases over time, the acceleration is considered positive. This means that the body is moving in the direction of its positive axis.
- Negative Acceleration: If the body's velocity decreases over time, the acceleration is considered negative. This means that the body is moving in the opposite direction of its positive axis.
- Uniform Acceleration: If the body's velocity increases or decreases at a constant rate, the acceleration is considered uniform. This means that the body's velocity changes by the same amount in each equal time interval.
4. Conclusion:
In the case of a body starting from rest, the initial velocity is zero. Therefore, the change in velocity (∆v) is equal to the final velocity (vf). If the body's velocity increases over time, the acceleration is considered positive. Hence, the correct answer is A: Positively accelerated.

The slope of the position-time graph gives the speed of the object.

Slope is given as
Slope = Position/Time
By definition, speed is given as distance divided by time.
Thus, slope of the position-time graph is speed of the object.

Explanation:
Uniform Circular Motion
When a body moves uniformly along a circle, it means that it moves with a constant speed and changes its direction continuously. This type of motion is called uniform circular motion.
Velocity and Speed
Velocity is a vector quantity that includes both magnitude (speed) and direction. Speed, on the other hand, is a scalar quantity that only includes magnitude. In uniform circular motion, the direction of the velocity is constantly changing, but the magnitude of the velocity (speed) remains constant.
Explanation of the options:
A: Its velocity changes but speed remains the same
- In uniform circular motion, the velocity changes because the direction of motion changes continuously.
- However, the speed remains the same because the magnitude of the velocity (speed) does not change.
B: Its speed changes but velocity remains the same
- This option is incorrect because in uniform circular motion, the speed remains constant while the velocity changes.
C: Both speed and velocity change
- This option is incorrect because the speed remains constant while only the direction of the velocity changes.
D: Both speed and velocity remain the same
- This option is incorrect because the velocity changes due to the continuous change in direction.
Therefore, the correct answer is A: Its velocity changes but the speed remains the same.

The correct statement is A: speed and distance are scalar, velocity and displacement are vector.
Explanation:
- Scalar quantities only have magnitude (size or value) and no direction, while vector quantities have both magnitude and direction.
- Speed is a scalar quantity as it only represents the magnitude of the distance traveled per unit time.
- Distance is also a scalar quantity as it only represents the magnitude of the total length covered.
- Velocity, on the other hand, is a vector quantity as it represents magnitude (speed) as well as direction of motion.
- Displacement is also a vector quantity as it represents the magnitude and direction of the change in position from the initial to the final point.
Therefore, the correct statement is A: speed and distance are scalar, velocity and displacement are vector.