Find the acceleration of the particle at $x = 5\,m$ using the given $v^2-x$ graph,where $v$ is velocity and $x$ is displacement.

The motion of a particle is described by the equation $x = a + bt^2$ where $a = 15 \, cm$ and $b = 3 \, cm/s^2$. Its instantaneous velocity at time $t = 3 \, s$ will be ........ $cm/s$.

$A$ velocity-time graph of a body is shown below. The distance covered by the body from $t = 6 \ s$ to $t = 9 \ s$ is: (in $m$)

$A$ particle shows a distance-time curve as shown in the figure. The maximum instantaneous velocity of the particle is around the point:

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?

Match Column-$I$ with Column-$II$: