work done on a body = change in kinetic energy

This is not necessarily true. Yes, change in KE may be equal to the work performed, but if the body gains or loses any potential energy (moving vertically against the force of gravity, for example) it's change in KE will be different than the work performed. However, if KE is the only form of energy underconsideration, then consider that from Newton:

F = ma

So a force applied over a distance (the definition of work) gives:

W = Fd = mad

From the formula


v_2^2 - v_1^2 = 2ad


you can substitute to get:


W = Fd = \frac 1 2 m (2ad) = \frac 1 2 m(v_2^2 - v_1^2) = \Delta KE