The position $x$ of a particle varies with time $t$ as $x = ct^2 + b$,where $c$ and $b$ are positive constants. Which of the following graphs is correct?

In the following velocity-time graph,the distance travelled by the body in metres is ............. $m$.

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 following figure shows the variation of displacement $x$ with time $t$ for a particular object. Identify the correct interpretation of the graph.

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 figure shows a velocity-time graph of a particle moving along a straight line. The particle comes to rest at $t = \dots \text{sec}$.