Power applied to a particle varies with time as $P = (4t^3 -5t + 2)\,watt$, where $t$ is in  second. Find the change is its $K.E.$ between time $t = 2$ and $t = 4 \,sec.$ ............... $\mathrm{J}$

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 

Pulley and spring are massless and the friction is absent everwhere. $5\,kg$ block is released from rest. The speed of $5\,kg$ block when $2\,kg$ block leaves the contact with ground is (take force constant of the spring $K = 40\,N/m$ and $g = 10\,m/s^2$ )

Adjacent figure shows the force-displacement graph of a moving body, what is the work done by this force in displacing body from $x = 0$ to $x = 35\,m$ ? ........... $\mathrm{J}$

A ball of mass $M$ falls from a height $h$ on a floor which the coefficient of restitution is $e$. The height attained by the ball after two rebounds is

A body constrained to move along $y-$ axis is subjected to a constant force $\vec F =  - \hat i + 2\hat j + 3\hat k\,N$ The work done by this force in moving the body a distance of $4\, m$ along $y-$ axis is ............... $\mathrm{J}$