Centripetal acceleration is the acceleration of a body that is traveling 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 produce an acceleration.

Derivation:

F=mv ² /r(using centripetal force)

Also, F=ma(using newton’s 2 ^nd law)

We can rewrite it as a=Fm

Substituting the value in the above equation,

a=mv ² /r/m

Simplifying it, we get

a=v ² /r