The distance travelled by a particle is related to time $t$ as $x = 4t^2$. The velocity of the particle at $t = 5 \, s$ is $......... \, ms^{-1}$.

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.

$A$ train moves from one station to another in $2$ hours. Its speed-time graph during this motion is shown in the figure. The maximum acceleration during the journey is ............. $km\, h^{-2}$.

For the velocity-time graph shown in the figure,the distance covered by the body in the last two seconds of its motion is $S_1$. What is the ratio of $S_1$ to the total distance covered by it?

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

The $x-t$ equation is given as $x = 2t + 1$. The corresponding $v-t$ graph is: