Work done, W = F x s
By Newton's second law, F = ma
W = ma x s
where, a = acceleration
Using equation of motion v2 - u2 =2as, we get
(v2-u2)/2 = as
W = m x (v2 - u2)/2
As intial velocity is zero, W = ½mv2
This work done is stored as kinetic energy of the object.
So, KE = ½ mv2