The velocity-time graph of a body falling from rest under gravity and rebounding from a solid surface is represented by which of the following graphs?

Among the four graphs shown in the figure,there is only one graph for which the average velocity over the time interval $(0, T)$ can vanish for a suitably chosen $T$. Which one is it?

$A$ particle starts from the origin at time $t = 0$ and moves along the positive $x-$ axis. The velocity-time graph is shown in the figure. What is the position of the particle at time $t = 5\,s$ (in $,m$)?

The graph between the displacement $x$ and time $t$ for a particle moving in a straight line is shown in the figure. Determine the sign of the acceleration of the particle for the intervals $OA$,$AB$,$BC$,and $CD$ respectively.

The acceleration-time graph for a body is shown in the graph. Which of the following graphs would probably represent the velocity of the body plotted against time?

In the following displacement $x$ versus time $t$ graph,at which among the points $P, Q$ and $R$ is the object's speed increasing?