$A$ particle moves along a straight line in such a way that its acceleration is increasing at the rate of $2 m/s^3$. Its initial acceleration and velocity were $0$. The distance covered by it in $t = 3 s$ is ........ $m$.

The same retarding force is applied to stop a train. The train stops after $80 \ m$. If the speed is doubled,then the stopping distance will be

$A$ three-wheeler starts from rest,accelerates uniformly with $1\; m/s^{2}$ on a straight road for $10\; s$,and then moves with uniform velocity. Plot the distance covered by the vehicle during the $n^{\text{th}}$ second $(n = 1, 2, 3, \ldots)$ versus $n$. What do you expect this plot to be during accelerated motion: a straight line or a parabola?

An object moving along the $x$-axis with a uniform acceleration has a velocity $\vec{v} = (12 \ cm \ s^{-1}) \hat{i}$ at $x = 3 \ cm$. After $2 \ s$,if it is at $x = -5 \ cm$,then its acceleration is:

$A$ graph between the square of the velocity of a particle and the distance $s$ moved by the particle is shown in the figure. The acceleration of the particle is $...........m/s^2$.

$A$ particle initially at rest is moving along a straight line with an acceleration of $2 \,m/s^2$. At a time of $3 \,s$ after the beginning of motion, the direction of acceleration is reversed. The time from the beginning of the motion in which the particle returns to its initial position is