Centripetal acceleration is the acceleration of a body that is travelling across a circular path. When a body undergoes a circular motion, its direction constantly changes and thus its velocity changes (velocity is a vector quantity) which produces an acceleration.Derivation:

F=mv2r (using centripetal force)

F=ma (using Newton's second law)

We can rewrite this as:

a=Fm

Substituting the value of F 

$a=\frac{m v^2}{r} \div m$

a=v2r

Thus, the centripetal acceleration is given by a=v2r.