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.

Explanation

Les s be the distance covered by the body moving in the direction of constant force F. Work done by this force on the body,
W = F s ........(i)
If a is the acceleration produced in the body of mass m due to this constant force F and if its velocity changes from u to `upsilon` then
F = ma.....(ii)
and `upsilon^2 - u^2 = 2 as or s = (upsilon^2 - u^2)/(2a) ..... (iii)`
From eqns. (i), (ii) and (iii), `W = (ma)((upsilon^2- u^2)/(2a)) = (1)/(2)mupsilon^2 - (1)/(2)mu^2`
Since `(1)/(2)mupsilon^2 - (1)/(2)mu^2` = final kinetic energy - initial kinetic energy
= increases in kinetic energy,
Work done, W = increases in kinetic energy.