Instantaneous acceleration is a vector, so it can be split up into two perpendicular vectors in such a way that their sum is instantaneous velocity.  

These vectors are:

   - one tangential to the trajectory: tangential acceleration

   - another perpendicular to tangential acceleration: normal or centripetal acceleration

Why is instantaneous acceleration split into two perpendicular vectors, one tangential to the trajectory at each point and another perpendicular? 

      In fact, it is a mathematical necessity which you may not yet understand, which is that acceleration is the derivative of the velocity vector with respect to time.    

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