The given graph shows the variation of velocity with displacement. Which one of the graphs given below correctly represents the variation of acceleration with displacement?

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

The position $x$ of a particle with respect to time $t$ along the $x$-axis is given by $x = 9t^2 - t^3$,where $x$ is in metres and $t$ is in seconds. What will be the position of this particle when it achieves maximum speed along the $x$-direction?

The figure shows a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion,give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A, B, C$ and $D$?

The velocity-displacement graph of a particle moving in a straight line is as shown in the figure.

$y = (P t^2 - Q t^3) \ m$ is the vertical displacement of a ball which is moving in a vertical plane. Then the maximum height that the ball can reach is,