$A$ particle of mass $500 \,g$ is moving in a straight line with velocity $v = b x^{5/2}$. The work done by the net force during its displacement from $x = 0$ to $x = 4 \,m$ is ................... $J$ (Take $b = 0.25 \,m^{-3/2} s^{-1}$)

The rain drop of mass $1 \text{ g}$,starts with zero velocity from a height of $1 \text{ km}$. It hits the ground with a speed of $5 \text{ m/s}$. The work done by the unknown resistive force is . . . . . . $J$. (take $g = 10 \text{ m/s}^2$)

$A$ heavy stone is thrown with speed $v$ from a cliff of height $h$. How and in which direction should it be thrown so that the stone hits the ground with maximum speed?

$A$ lorry and a car moving with the same kinetic energy $(K.E.)$ are brought to rest by applying the same retarding force. Then:

$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest,the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given,moment of inertia of sphere $= \frac{2}{5} mr^2$].

If work is positive,then kinetic energy increases or decreases?