$A$ 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?

On what factors does the stopping distance depend?

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s)-$ velocity $(v)$ graph of this object is

The motion of a particle along a straight line is described by the equation $x = 8 + 12t - t^3$,where $x$ is in meters and $t$ is in seconds. The retardation of the particle when its velocity becomes zero is .......... $m/s^2$.

$A$ particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x$-axis. Identify all figures that correctly represent the motion qualitatively. ($a =$ acceleration,$v =$ velocity,$x =$ displacement,$t =$ time)

The initial velocity of a particle is $u$ at $t=0$ and the acceleration $a$ is given by $a = \alpha t^{3/2}$. Which of the following relations is valid?