$(i)$ Define power. Mention its $SI$ unit.
$(ii)$ $A$ boy of mass $50 \, kg$ runs up a staircase of $40$ steps in $8 \, s$. If the height of each step is $15 \, cm$,find his power. (Given,$g = 10 \, m \, s^{-2}$)

$A$ boy pushes the wall in the class for five minutes but the wall does not move. Another boy pushes the chair from the front to the back side of the class. In which case,more work is done?

When a body falls freely towards the earth,then its total energy

Four persons jointly lift a $250 \,kg$ box to a height of $1 \,m$ and hold it.
$(a)$ Calculate the work done by the persons in lifting the box.
$(b)$ How much work do they do just holding it?
$(c)$ Why do they get tired while holding it? $(g = 10 \,m/s^2)$

The velocity of a body moving in a straight line is increased by applying a constant force $F$ for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.

$A$ box of mass $10 \, kg$ is placed at point $A$ on a horizontal surface. It is moved to point $B$,which is at a distance of $2 \, m$ from $A$. If the line joining $A$ and $B$ is horizontal,find the work done by the gravitational force on the box. Justify your answer. $(g = 10 \, m s^{-2})$ (in $, J$)