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

A particle moves along a straight line. Its position at any instant is given by $x=32 t-\frac{8 t^3}{4}$, where $x$ is in metre and $t$ is in second. Find the acceleration of the particle at the instant when particle is at rest $..........\,m / s ^2$

$Assertion$ : A body with constant acceleration always moves along a straight line.

$Reason$ : A body with constant acceleration may not speed up.

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

The velocity time graph of a body is shown in Figure. It implies that at point $B$ :-

A particle initially at rest starts moving from reference point. $\mathrm{x}=0$ along $\mathrm{x}$-axis, with velocity $v$ that varies as $v=4 \sqrt{\mathrm{x} m} / \mathrm{s}$. The acceleration of the particle is __________$ \mathrm{ms}^{-2}$.