If the velocity-time graph has the shape \(AMB,\) what would be the shape of the corresponding acceleration-time graph?

 

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An engine of a train moving with uniform acceleration passes the signal post with velocity \(u\) and the last compartment passes the same post with velocity \(v\). The velocity with which the middle point of the train passes the signal post is:

A body is projected vertically upward and then allowed to fall back down under gravity. Which of the following velocity–time \((v \text-t) \) graphs correctly represents its motion throughout the ascent and descent?

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A scooter accelerates from rest for time \(t_1\) at constant rate \(a_1\) and then retards at constant rate \(a_2\) for time \(t_2\) and comes to rest. The correct value of  \(\frac{t_1}{t_2}\) will be:
1. \(\frac{a_1+a_2}{a_2}\)
2. \(\frac{a_2}{a_1}\)
3. \(\frac{a_1}{a_2}\)
4. \(\frac{a_1+a_2}{a_1}\)

Two stones are thrown simultaneously from the edge of a cliff \(240~\text{m}\) high. The first stone is thrown upward with an initial speed of \(10~\text{m/s},\) and the second with \(40~\text{m/s}.\) Assuming the stones do not bounce after hitting the ground and neglecting air resistance (\(g= 10~\text{m/s}^2\)), which of the following graphs best represents how the position of the second stone varies relative to the first stone with time? (graphs are schematic and not drawn to scale)

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From a tower of height \(H\), a particle is thrown vertically upwards with a speed \(u\). The time taken by the particle, to hit the ground, is \(n\) times that taken by it to reach the highest point of its path. The relation between \(H,u\) and \(n\) is:
1. \( g H=(n-2)^2 u^2 \)
2. \( 2{gH}={nu}^2({n}-2) \)
3. \( g H=(n-2) u^2 \)
4. \( 2{gH}={n}^2{u}^2\)

The four graphs below are intended to represent the same motion. However, one of them is incorrect. Identify the graph that does not accurately depict the motion.

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A stone is dropped from the top of a building. When it crosses a point \(5\) m below the top, another stone starts to fall from a point \(25\) m below the top. Both stones reach the bottom of the building simultaneously. The height of the building is:
1. \(35~\text{m}\)
2. \(45~\text{m}\)
3. \(50~\text{m}\)
4. \(25~\text{m}\)

A tennis ball is released from a height \(h\) and after freely falling on a wooden floor it rebounds and reaches height \(\frac{h}{2}\). The velocity versus height of the ball during its motion may be represented graphically by:
(graph are drawn schematically and on not to scale)

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The velocity (\(v\)) and time (\(t\)) graph of a body in a straight-line motion is shown in the figure. The point \(S\) occurs at \(4.333\) seconds. The total distance covered by the body in \(6\) s is:

       
1. \(12\) \(\text{m}\)
2. \(\dfrac{49}{12}\) \(\text{m}\)
3. \(11\) \(\text{m}\)
4. \(\dfrac{37}{3}\) \(\text{m} \)