Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $watt$ . Here, $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$, the velocity of particle at time $t = 2\, s$ will be ………… $\mathrm{m}/ \mathrm{s}$

A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

If a spring extends by $x$ on loading then energy stored by the spring is ($T$ is tension in spring, $K$ is spring constant)

A mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass initially at rest. After collision the first mass moves with velocity $\frac{v}{\sqrt 3}$ in a  direction perpendicular to its initial direction of motion. The speed of second mass after collision is 

A ball is dropped from height $h$ on a plane. If the coefficient of restitution of the plane is $e$ and if ball hits ground two times, the height upto which it reaches after two jumps, will be