The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $\mathrm{x}^{2}=\mathrm{at}^{2}+2 \mathrm{bt}+\mathrm{c.}$ If the acceleration of the particle depends on $\mathrm{x}$ as $\mathrm{x}^{-\mathrm{n}},$ where $\mathrm{n}$ is an integer, the value of $\mathrm{n}$ is

The velocity of a body depends on time according to the equation $v=\frac{t^2}{10}+20$. The body is undergoing

The velocity $v$ of a body moving along a straight line varies with time $t$ as $v=2 t^2 e^{-t}$, where $v$ is in $m / s$ and $t$ is in second. The acceleration of body is zero at $t=$