$A$ particle moves along a straight line $OX$. At a time $t$ (in seconds),the distance $x$ (in metres) of the particle from $O$ is given by $x = 40 + 12t - t^3$. How long would the particle travel before coming to rest?

$A$ car accelerates from rest at a constant rate $\alpha$ for some time,after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is $t$,then the maximum velocity acquired by the car is

The velocity of a particle moving in the positive direction of the $x$-axis varies as $v = 5 \sqrt{x}$. Assuming that at $t = 0$,the particle was at $x = 0$,what is the acceleration of the particle in $m/s^2$?

$A$ body falling for $2 \, s$ covers a distance $S$ equal to that covered in the next second. Taking $g = 10 \, m/s^2$,$S = .......... m$

Two bodies $A$ and $B$ move in the same straight line starting from the same position. Body $A$ moves with a constant velocity $u$ and body $B$ moves with a constant acceleration $a$ starting from rest. When their velocities become equal,the distance between them is:

$A$ particle starting from rest and moving with a uniform acceleration along a straight line covers distances $a$ and $b$ in successive intervals of $p$ and $q$ seconds. The acceleration of the particle is