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Q. No.In some appropriate units, time \((t)\) and position \((x)\) relation of a moving particle is given by \(t=x^2+x. \) The acceleration of the particle is:
| 1. | \(+\dfrac{2}{(x+1)^3}\) | 2. | \(+\dfrac{2}{(2x+1)}\) |
| 3. | \(-\dfrac{2}{(x+2)^3}\) | 4. | \(-\dfrac{2}{(2x+1)^3}\) |
Subtopic: Non Uniform Acceleration |
Level 3: 35%-60%
NEET - 2025
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Two cities \(X \) and \(Y\) are connected by a regular bus service with a bus leaving in either direction every \(T~\text{min}.\) A girl is driving scooty with a speed of \(60~\text{km/h}\) in the direction \(X\) to \(Y\) notices that a bus goes past her every \(30~\text{minutes}\) in the direction of her motion, and every \(10~\text{minutes}\) in the opposite direction. Choose the correct option for the period \(T\) of the bus service and the speed (assumed constant) of the buses.
1. \(10 ~\text{min},~ 90~ \text{km/h}\)
2. \(15 ~\text{min},~ 120~ \text{km/h}\)
3. \(9 ~\text{min},~ 40~ \text{km/h}\)
3. \(25 ~\text{min},~ 100~ \text{km/h}\)
1. \(10 ~\text{min},~ 90~ \text{km/h}\)
2. \(15 ~\text{min},~ 120~ \text{km/h}\)
3. \(9 ~\text{min},~ 40~ \text{km/h}\)
3. \(25 ~\text{min},~ 100~ \text{km/h}\)
Subtopic: Relative Motion in One Dimension |
54%
Level 3: 35%-60%
NEET - 2025
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The velocity \((v)\)-time \((t)\) plot of the motion of a body is shown below:
The acceleration \((a)\)-time \((t)\) graph that best suits this motion is:
The acceleration \((a)\)-time \((t)\) graph that best suits this motion is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Graphs |
77%
Level 2: 60%+
NEET - 2024
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An object falls freely from height \(h\) above the ground. It travels \(\dfrac{5}{9}h\) of the total height in the last \(1~\text{s}.\) The height \(h\) is: \( \left (\text{use}~g =10~\text{m/s}^{2} \right )\)
| 1. | \(5~\text{m}\) | 2. | \(25~\text{m}\) |
| 3. | \(45~\text{m}\) | 4. | \(58~\text{m}\) |
Subtopic: Uniformly Accelerated Motion |
67%
Level 2: 60%+
NEET - 2024
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A body is falling freely in a resistive medium. The motion of the body is described by \(\dfrac{dv}{dt}=(4-2v), \) where \(v\) is the velocity of the body at any instant (in \(\text{ms}^{–1}\)). The terminal velocity in this case refers to the velocity the body approaches as time \(t \to \infty.\) The initial acceleration and terminal velocity of the body, respectively, are:
| 1. | \(4~\text{m/s}^2,\) \(2~\text{m/s}\) | 2. | \(2~\text{m/s}^2,\) \(4~\text{m/s}\) |
| 3. | \(6~\text{m/s}^2,\) \(2~\text{m/s}\) | 4. | \(2~\text{m/s}^2,\) \(6~\text{m/s}\) |
Subtopic: Acceleration |
64%
Level 2: 60%+
NEET - 2024
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The speed \((s)\) of a car as a function of time \((t)\) is shown figure, The distance travelled by the car in \(8\) seconds is:
| 1. | \(180~\text{m}\) | 2. | \(60~\text{m}\) |
| 3. | \(80~\text{m}\) | 4. | \(18~\text{m}\) |
Subtopic: Graphs |
81%
Level 1: 80%+
NEET - 2024
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A particle is moving along the \(x\text-\)axis with its position \((x)\) varying with time \((t)\) as \(x=\alpha t^{4}+\beta t^{2}+\gamma t+\delta.\) The ratio of its initial velocity to its initial acceleration is:
1. \(2\alpha:\delta \)
2. \(\gamma:2\delta \)
3. \(4\alpha:\beta \)
4. \(\gamma:2\beta \)
1. \(2\alpha:\delta \)
2. \(\gamma:2\delta \)
3. \(4\alpha:\beta \)
4. \(\gamma:2\beta \)
Subtopic: Instantaneous Speed & Instantaneous Velocity |
77%
Level 2: 60%+
NEET - 2024
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A vehicle travels half the distance with speed \(v\) and the remaining distance with speed \(2v.\) Its average speed is:
| 1. | \(\dfrac{3v}{4}\) | 2. | \(\dfrac{v}{3}\) |
| 3. | \(\dfrac{2v}{3}\) | 4. | \(\dfrac{4v}{3}\) |
Subtopic: Average Speed & Average Velocity |
70%
Level 2: 60%+
NEET - 2023
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A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \(4\) ms–1. The ball strikes the water surface after \(4\) s. The height of bridge above water surface is: (Take \(g=10~ \text {ms}^{-2}\) )
| 1. | \(68\) m | 2. | \(56\) m |
| 3. | \(60\) m | 4. | \(64\) m |
Subtopic: Uniformly Accelerated Motion |
69%
Level 2: 60%+
NEET - 2023
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The displacement-time \((s\text-t)\) graphs of two moving particles \(A~\text{and}~B\) make angles of \(30^\circ\) and \(45^\circ\) with the \(x\text-\)axis as shown in the figure. The ratio of their respective velocity \(\left(\dfrac{v_A}{v_B}\right) \) is:
1. \(1: \sqrt{3}\)
2. \(\sqrt{3}: 1\)
3. \(1:1\)
4. \(1:2\)
1. \(1: \sqrt{3}\)
2. \(\sqrt{3}: 1\)
3. \(1:1\)
4. \(1:2\)
Subtopic: Graphs |
75%
Level 2: 60%+
NEET - 2022
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