Work done in time $t$ on a body of mass $m$  which is accelerated from rest to a speed $v$  in time $t_1$  as a function of time $t$  is given by

State if each of the following statements is true or false. Give reasons for your answer.

$(a)$ In an elastic collision of two bodies, the momentum and energy of each body is conserved.

$(b)$ Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.

$(d)$ In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

A body of mass $m$ is projected from ground with speed $u$ at an angle $\theta$ with horizontal. The power delivered by gravity to it at half of maximum height from ground is

The work done by a force $\vec F = \left( { – 6{x^3}\hat i} \right)\,N$ in displacing a particle from $x = 4\,m$ to $x = -2\,m$ is …………… $\mathrm{J}$

The force acting on a body moving along $x-$ axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at