Formula for kinetic energy || kinetic energy formula || Derivation of kinetic energy ||

 Kinetic Energy of a body can be obtained either from

(i) the amount of work done in stopping the moving body, or from

(ii) the amount of work done in giving the present velocity to the body from the state of rest. 

Let us use the second method:

Suppose, m = mass of a body at rest (i.e., u=0).

                  F = Force applied on the body

                  a = acceleration produced in the body                            in the direction of force applied. 

                 v = velocity acquired by the body in                               moving through a distances. 

From, 

                v²- u² = 2 a s

                v²- 0 = 2 a s

                  a = v² / 2 a s          .... (i) 

As    F = m a          .: using eq (i) 

        F = m (v² / 2 a s) 

Work done on the body, W = force×displacement

    W = m × v² / 2 s × s

    W = 1/2 m v²

This work done on the body is a measure of kinetic energy {K•E} acquired by the body. 

Kinetic energy of body = W = 1/2 m v².