A particle of mass $7\, kg$ moving at $5\, m/s$ is acted upon by a variable force opposite to its initial direction of motion. The variation of force $F$ is shown as a function of time $t$.

An object has momentum $p$ & kinetic energy $E$. If its momentum becomes $2\,p$ then  its kinetic energy will be :-

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 body of mass $m= 10^{-2} \;kg$ is moving in a medium and experiences a frictional force $F= -kv^2$ Its intial speed is $v_0= 10$ $ms^{-1}$ If, after $10\ s$, its energy is $\frac{1}{8}$ $mv_0^2$ the value of $k$ will be

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.