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: 
1. 2.
3. 4.
Subtopic:  Graphs |
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An object falls freely from height \(h\) above the ground. It travels \(\dfrac{5}{9}h\) in the last \(1~\text{s}\). Then height \(h\) is: (Given \(g =10~\text{ms}^{-2}\)
1. \(5~\text{m}\) 2. \(25~\text{m}\)
3. \(45~\text{m}\) 4. \(58~\text{m}\)
Subtopic:  Uniformly Accelerated Motion |
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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:  Distance & Displacement |
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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. \(\gamma:2\beta \)
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
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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. \(\frac{3v}{4}\)
2. \(\frac{v}{3}\)
3. \(\frac{2v}{3}\)
4. \(\frac{4v}{3}\)
Subtopic:  Average Speed & Average Velocity |
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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 |
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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. \(1:2\)
Subtopic:  Graphs |
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The ratio of the distances travelled by a freely falling body in the \(1\)st, \(2\)nd, \(3\)rd and \(4\)th second is:
1. \(1:1:1:1\)
2. \(1:2:3:4\)
3. \(1:4:9:16\)
4. \(1:3:5:7\)
Subtopic:  Uniformly Accelerated Motion |
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A stone is thrown vertically downwards with an initial velocity of \(40\) m/s from the top of a building. If it reaches the ground with a velocity of \(60\) m/s, then the height of the building is: (take \(g=10\) m/s2)
1. \(120\) m
2. \(140\) m
3. \(80\) m
4. \(100\) m

Subtopic:  Uniformly Accelerated Motion |
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The figure given below shows the displacement and time, \((x\text -t)\) graph of a particle moving along a straight line:
           
The correct statement, about the motion of the particle, is:

1. the particle moves at a constant velocity up to a time \(t_0\) and then stops.
2. the particle is accelerated throughout its motion.
3. the particle is accelerated continuously for time \(t_0\) then moves with constant velocity.
4. the particle is at rest.

Subtopic:  Graphs |
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