The spacecraft of mass $M$ moves with velocity $V$ in free space at first, then it explodes breaking  into two pieces. If after explosion a piece of mass $m$ comes to rest, the other piece of space craft will have a velocity

In one dimensional case, the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $\mathrm{ergs}$

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 $t = 2s$ will be ............. $\mathrm{m}/ \mathrm{s}$

The total work done on a particle is equal to the change in its kinetic energy. This is applicable

A mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is

When a constant force is applied to a body moving with constant acceleration, power does not remain constant. For power to be constant, the force has to vary with speed as follows