Test: Motion- 2 - UPSC MCQ

In figure A, we can see that the object continues to remain at a fixed place while the time keeps running. So, the object is at rest, because the object does not change its position with time.

- Assertion is false: Acceleration can be negative, positive, or zero, depending on whether the velocity of the body is decreasing, increasing, or constant, respectively.
- Reason is true: Acceleration is indeed the rate of change of velocity.
- Correct option: D. The assertion is false, but the reason is true. Acceleration is not limited to being positive; it reflects any change in velocity's magnitude or direction.

The car travels in two segments:

• First segment: 30 km at 60 km/hr
• Second segment: 90 km at 30 km/hr

To find the average speed, use the formula:

Average Speed = Total Distance / Total Time

Total Distance: 30 km + 90 km = 120 km

Time for First Segment: 30 km / 60 km/hr = 0.5 hours

Time for Second Segment: 90 km / 30 km/hr = 3 hours

Total Time: 0.5 hours + 3 hours = 3.5 hours

Now, calculate the average speed:

Average Speed = 120 km / 3.5 hours ≈ 34.29 km/hr

The answer is A.

The average acceleration can be calculated using the formula:

• Acceleration = (Final velocity - Initial velocity) / Time

First, convert the speeds from km/hr to m/s:

• 36 km/hr = 10 m/s
• 18 km/hr = 5 m/s
• 54 km/hr = 15 m/s

Calculate the change in velocity:

• Initial velocity (u) = 10 m/s
• Final velocity (v) = 15 m/s
• Total time = 9 seconds

Now, apply the values into the acceleration formula:

• Acceleration = (15 m/s - 10 m/s) / 9 s = 5 m/s / 9 s ≈ 0.56 m/s²

The average acceleration over the entire 9 seconds is approximately:

• 0.5 m/s²

v = u + at
or = 2m/s²
s = ut + 
= 100 m

The total distance travelled and the displacement can be calculated as follows:

• Distance: To find the distance for 3 revolutions, first calculate the circumference of the circular track:
  • Circumference = 2 × π × radius
  • Circumference = 2 × 3.14 × 14 m = 87.92 m
• Total distance for 3 revolutions = 3 × 87.92 m = 263.76 m

• Displacement: Since the cyclist returns to the starting point after 3 full revolutions, the displacement is:
  • Displacement = 0 m

Thus, the final values are:

• Distance: 263.76 m
• Displacement: 0 m

The magnitude of the displacement of an object is always:

• less than or equal to the distance travelled.

At maximum height, v = 0 m/s, u = 15 m/s, a = -10 m/s².

v = u + at

→ 0 = 15 + (-10)t

→ 0 = 15 - 10t

→ t = 15 / 10 = 1.5 s.

Thus, the time taken to reach maximum height is 1.5 seconds.

- The assertion is true. Displacement can be zero if an object returns to its starting point, despite having traveled some distance.
- The reason is false. Displacement is the shortest distance between the initial and final positions, not the longer distance.
- Therefore, the correct answer is C: A is true but R is false.

The equations of motion are applicable only when the body moves with uniform acceleration. A body under constant acceleration is uniformly accelerated motion.

Topic in NCERT: Equations of Motion

Line in NCERT: "The motion of an object moving at uniform acceleration can be described with the help of the following equations, namely v = u + at."

The wheel has a radius of 2 m, which gives it a circumference of:

• Circumference = 2 × π × radius = 2 × 3.14 × 2 = 12.56 m

In 10 seconds, the wheel completes 5 revolutions. Therefore, the distance travelled in that time is:

• Distance = 5 revolutions × 12.56 m/revolution = 62.8 m

Now, we can calculate the speed:

• Speed = Distance / Time = 62.8 m / 10 s = 6.28 m/s

To find out how many revolutions it would complete in 30 seconds at the same speed:

• Distance in 30 seconds = Speed × Time = 6.28 m/s × 30 s = 188.4 m
• Revolutions = Distance / Circumference = 188.4 m / 12.56 m = 15 revolutions

Thus, the answers are:

• Speed = 6.28 m/s
• Revolutions in 30 seconds = 15

- Assertion (A) is false: The speedometer measures instantaneous speed, not average time or average speed.
- Reason (R) is true: Average velocity is indeed total displacement divided by total time.
- Thus, the correct answer is D: A is false but R is true.
- A speedometer shows how fast a vehicle is moving at a specific moment, not over an entire trip.

Assertion (A): Incorrect. On a velocity-time graph, uniform acceleration is represented by a straight line, not a parabolic trajectory. A parabolic trajectory is seen on a position-time graph for uniformly accelerated motion.
Reason (R): Incorrect. The distance-time graph for uniform acceleration is not a straight line but a curve. A straight-line distance-time graph indicates uniform velocity, not acceleration.
Explanation: Both the Assertion and Reason are false. The Assertion is incorrect because uniform acceleration on a velocity-time graph is a straight line. The Reason is incorrect as well because uniform acceleration produces a curved distance-time graph.

In uniform circular motion, the object's speed remains constant, but its direction continuously changes. This change in direction means that the velocity is always changing, even though its magnitude remains constant. Thus, the acceleration is always directed towards the center of the circle, causing a change in velocity due to the change in direction.

Topic in NCERT: Uniform Circular Motion

Line in NCERT: "When an object moves in a circular path with uniform speed, its motion is called uniform circular motion."

It is horizontal so, angle is zero and also acceleration is zero. Hence constant velocity.

Topic in NCERT: VELOCITY-TIME GRAPHS

Line in NCERT: "If the object moves at uniform velocity, the height of its velocity-time graph will not change with time."