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Q. No.
A particle moves along a straight line so that its velocity \((v)\) is directed towards a fixed point on its path and is proportional to its distance \((x) \) from that point. Its acceleration is proportional to:
1. \(x \) 2. \(\dfrac1x \)
3. \(\sqrt x \) 4. \(\dfrac{1}{\sqrt x} \)
Subtopic:  Non Uniform Acceleration |
 63%
Level 2: 60%+
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A boy throws a ball straight up the side of a building and receives it after \(4~\text s.\) On the other hand, if he throws it so that it strikes a ledge on its way up, it returns to him after \(3~\text s.\) The ledge is at a distance \(d\) below the highest point, where \(d=? \) (take acceleration due to gravity, \(g=10~\text{ms}^{-2})\)

1. \(5~\text m\) 2. \(2.5~\text m\)
3. \(1.25~\text m\) 4. \(10~\text m\)
Subtopic:  Uniformly Accelerated Motion |
Level 3: 35%-60%
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A man driving a scooter at \(15~\text{m/s}\) brakes at the rate of \(2~\text{m/s}^2\). His speed, after \(10~\text{s}\) after the application of brakes will be:
1. \(5~\text{m/s}\)
2. \(-5~\text{m/s}\)
3. \(0~\text{m/s}\)
4. \(10~\text{m/s}\)

Subtopic:  Uniformly Accelerated Motion |
Level 3: 35%-60%
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A particle moves around a circle with a unique uniform speed in each revolution. After the first revolution and during the \(2^{\mathrm{nd}}\) revolution: its speed doubles; and during the \(3^{\mathrm{rd}}\) revolution, its speed becomes \(3\) times the initial speed and so on. The time for the \(1^{\mathrm{st}}\) revolution is \(12\) s. The average time per revolution for the first four revolutions, is:
1. \(4.8\) s
2. \(9.6\) s
3. \(6.25\) s
4. \(6\) s

Subtopic:  Average Speed & Average Velocity |
 70%
Level 2: 60%+
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Which of the following statements is true about the motion depicted in the diagram? 
              
1. The acceleration is constant and non-zero.
2. The velocity changes suddenly during the motion.
3. The velocity is positive throughout.
4. All of the above are true.
Subtopic:  Graphs |
 65%
Level 2: 60%+
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A particle is projected vertically upwards with a speed \(u\) and moves under the force of gravity. The distance travelled by the particle during its entire motion (until it returns) is \(d_1.\) If the force of gravity were to be switched off, and the particle travelled for the same length of time, then the distance travelled is \(d_2.\) Then, 
1. \(d_2 = d_1\)
2. \(d_2 = 2d_1\)
3. \(d_2 = 3d_1\) 
4. \(d_2 = 4 d_1\)
Subtopic:  Uniformly Accelerated Motion |
 55%
Level 3: 35%-60%
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The velocity-time graph of a particle, moving along a straight time, is shown in the figure. The curve, when plotted, takes the form of a 'circle'. The magnitude of the average acceleration of the particle is:
                   
1. \(1\) m/s2 
2. \(2\) m/s2
3. less than \(1\) m/s2
4. greater than \(2\) m/s2
Subtopic:  Acceleration |
 61%
Level 2: 60%+
Hints
Two cars \(A\) and \(B\) start moving along the same straight road, from the same point, simultaneously. The first car \((A)\) accelerates uniformly to a maximum speed of \(v_0\) and then decelerates uniformly to a stop. The second car \((B)\) accelerates uniformly to the same maximum speed \(v_0\) and then decelerates uniformly to a stop. The acceleration of \(A\) is twice that of \(B,\) and they both spend the same total time during the motion. Then,
(A) distance travelled by \(A\) = distance travelled by \(B\)
(B) acceleration time of \(A\) = \(\dfrac12\) acceleration time of \(B\)
(C) relative velocity of \(A\) with respect to \(B\) is always positive
(D) deceleration time of \(A\) = \(2×\) deceleration time of \(B\)

Choose the correct option from the given ones:
1. (A) is True.
2. (A), (B) are True.
3. (A), (B), (C) are True.
4. (B), (C), (D) are True.
Subtopic:  Acceleration |
Level 3: 35%-60%
Hints
A ball \((A)\) is projected vertically upward; a second ball \((B)\) is projected horizontally with the same initial speed as the first. The relative velocity of ball \(A\)  with respect to \(B\):
1. is constant in magnitude only
2. is constant in direction
3. is constant in magnitude and direction
4. varies, both in magnitude and direction
Subtopic:  Relative Motion in One Dimension |
Level 3: 35%-60%
Hints
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A particle moves along a straight line such that its velocity is proportional to the square root of its displacement. Its acceleration is:
1. zero
2. constant
3. proportional to time
4. proportional to displacement
Subtopic:  Acceleration |
 69%
Level 2: 60%+
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