Lakhmir Singh & Manjit Kaur Test: Motion - Class 9 MCQ

Vector Quantity

• Direction: A vector quantity has a specific direction in space. This means that not only does it have a magnitude, but it also has a specific orientation or direction in which it is pointing.
• Magnitude: In addition to having a direction, a vector quantity also has a magnitude. This magnitude represents the size or strength of the vector, indicating how much of the quantity is present.
• Both Magnitude and Direction: Therefore, a vector quantity possesses both magnitude and direction, distinguishing it from scalar quantities which only have magnitude. This dual nature of vectors allows for a more detailed description of physical quantities.

 

Odometer of automobiles records distance travelled: The primary function of an odometer in automobiles is to measure and display the total distance the vehicle has traveled since it was first put into use. This distance is usually displayed in kilometers or miles depending on the unit system used in the region.

According to the graph given, the body A does not have uniform motion. An object is said to be in uniform motion when it covers equal distances in equal intervals of time. In this case, it accelerates to a particular velocity and remains the same continuously. Otherwise, it is evident that the velocity of B is lesser that A initially and the body B crosses A at X.
Hence, the statement A has uniform motion is not correct.

Speedometer Measurement
- Instantaneous Speed: The speedometer of a car measures the instantaneous speed at any given moment.
- It provides a real-time reading of how fast the car is moving at that particular moment.
- This measurement is important for drivers to ensure they are following speed limits and driving safely.
- It helps drivers make adjustments to their speed based on road conditions, traffic, and other factors.

Option C is correct.
Explanation:

• Statement A: From the x-t graph, the slope of the line OA represents the velocity vOA, which is less than the velocity vAB. This is because the slope of the line AB is steeper than the slope of line OA, indicating a higher velocity.
• Statement B: The velocity vBC is negative because the slope of the line BC is negative, indicating motion in the negative direction on the x-axis.
• Statement C: The velocity vCD is the least by magnitude because the slope of the line CD is the least steep, indicating the smallest velocity compared to the other sections of the graph.
• Statement D: The x-t graph does not provide information about acceleration. It only shows velocity changes over time. Therefore, statement D is not correct.

Option C is the correct option.

When the displacement-time graph is parallel to the time axis, the velocity of the particle is zero because the particle is at rest and its displacement is not changing with time.

The correct answer is: Only A and B are correct

Explanation:

Velocity-Time Graph Analysis:
- The slope of the velocity-time graph gives the acceleration of the particle.
- If the velocity-time graph is a straight line, the acceleration is constant.
- The acceleration can be calculated by finding the slope of the line.

Calculating Acceleration:
- The acceleration can be calculated using the formula: acceleration = change in velocity / change in time.
- By looking at the graph, we can see that the change in velocity is 10 m/s and the change in time is 4 seconds.

Acceleration Calculation:
- acceleration = change in velocity/ time
- acceleration = 10-5 / 2 = 2.5 m/s²

Therefore, the acceleration of the particle is 2.5 m/s². Hence, the correct answer is option D: 2.5 m/s²

The correct answer is D: Both (a) and (b).

• Acceleration is the rate of change of velocity. It can be positive (increasing velocity) or negative (decreasing velocity).
• Retardation is another term specifically used for negative acceleration. It describes a situation where the velocity is slowing down.

Therefore, when the velocity of a body is reducing, it has both:

• Negative acceleration: Because the change in velocity is negative.
• Retardation: Because it's the specific term for negative acceleration in the context of slowing down.

Option B is correct .

The maximum acceleration occurs during segment B to C as it has the steepest slope on the graph, representing the highest rate of change of velocity.

Option A is correct.

Explanation:

• From the x-t graph, we can see that the velocity of object A (V_A) is greater than the velocity of object B (V_B) at point x₁.
• If the slope of the tangent for A is greater than the slope of the tangent for B at x₁, then V_A> V_B at that point.

Explanation:

Displacement is the straightest shot (shortest distance) between start and end. Distance is the total path taken. Imagine going for a walk around a block - the displacement is the length of one side, while the distance is the entire walk. The numerical ratio of displacement to distance is calculated as displacement divided by distance. So the ratio:

• Can be 1 (straight path)
• Is less than 1 (curved path or going back and forth)
• Never more than 1

Therefore, the answer is D: equal to or less than 1.

The correct answer is C: zero displacement.

Explanation: 

• Displacement is the straight line distance between the starting and ending points of an object's motion.
• In this scenario, the body starts at A, goes to B, and then returns to A. Even though the body travels a certain distance (twice the distance between A and B), it ends up back at its starting point (A).
• Since displacement considers the net change in position, and the body ends at the same point it started, the displacement is zero.

In the given graph we find that the velocity is constant throughout, hence the object represented in the v - t graph is said to be in uniform motion.  Zero acceleration is also called uniform acceleration.

Option B is correct. 

In a distance-time graph, the slope or gradient. The greater the gradient, the greater the rate of change. of the line is equal to the speed of the object. The steeper the line (and the greater the gradient) the faster the object is moving.

Option B is correct. Car B is the slowest
-Car B covers the least distance in the same amount of time compared to the other cars, making it the slowest among the four.

Displacement = Area of ΔABC

Acceleration is the measure of how fast the velocity changes. Velocity is a vector quantity and a change in velocity is due to  change in magnitude or change in direction or both. Here,  the boy is moving with constant speed but velocity changes and hence is supposed to be in accelerated motion. 

Explanation:
Velocity-Time Graph Analysis:
The velocity-time graph shown depicts the motion of objects A and B.The collision between A and B occurs when their velocity is 10 ms^1.

Interpreting the Graph:The graph shows that the velocity of object A exceeds 10 ms^-1 at a certain point.This indicates that object A is moving faster than 10 ms-1 at that point.

Acceleration Analysis:Since the velocity of object A exceeds 10 ms-1, it implies that object A is accelerating.
Similarly, the behavior of object B on the graph also indicates non-zero acceleration.

Conclusion:
- Based on the analysis of the velocity-time graph, it can not  be concluded that both objects A and B have non-zero acceleration.
- Therefore, the correct answer is option B: both A and B have non-zero acceleration.