KE = 1/2 mv²

Consider an object of mass, m moving with a uniform velocity, u. Let it now be displaced through a distance s when a constant force, F acts on it in the direction of its displacement.  Work done, W is F s. The work done on the object will cause a change in its velocity. Let its velocity change from u to v. Let a be the acceleration produced. The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement,

s is v² – u² = 2a s

This gives

s = v² – u² /2a

Thus, work done by force F

= m a x (v² – u² /2a )

Or ½ m (v² – u²)

If the object is starting from its stationary position, that is, u = 0, then

W = ½ mv²

Therefore, work done is equal to the change in the kinetic energy of an object.

If u = 0, the work done will be ½ mv².

Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform

velocity, v is

E_k = ½ mv²