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

The initial velocity of a particle is $u$ (at $t = 0$) and the acceleration is given by $a(t) = at$. Which of the following relations is valid?

$A$ car starts from rest and moves with uniform acceleration. Describe the shapes of the $(i)$ $x-t$, $(ii)$ $v-t$, and $(iii)$ $a-t$ graphs for this motion.

Consider a particle moving along the positive direction of the $X$-axis. The velocity of the particle is given by $v = \alpha \sqrt{x}$ (where $\alpha$ is a positive constant). At time $t = 0$,the particle is located at $x = 0$. Find the time dependence of the velocity and the acceleration of the particle,respectively.

$A$ particle moving with uniform acceleration travels $24\, m$ and $64\, m$ in the first two consecutive intervals of $4\, s$ each. Its initial velocity is ....... $m/s$.

$A$ small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of $10 \, m$ in $t \, s$,the distance travelled by the toy in the next $t \, s$ will be ......... $m$.