Using the above results for the path properties in terms of s, the acceleration in the inertial reference frame as described in terms of the components normal and tangential to the path of the particle can be found in terms of the function s (t) and its various time derivatives (as before, primes indicate differentiation with respect to s) with: a ( s ) = d d t v ( s ) = d d t [ d s d t ( x ′ ( s ) , y ′ ( s ) ) ] = ( d 2 s d t 2 ) u t ( s ) + ( d s d t ) 2 ( x ″ ( s ) , y ″ ( s ) ) = ( d 2 s d t 2 ) u t ( s ) − − ( d s d t ) 2 1 ρ ρ u n ( s ) , as can be verified by taking the dot product with the unit vectors u t (s) and u n (s). This result for acceleration is the same as that for circular motion based on the radius ρ. Using this coordinate system in the inertial frame, it is easy to identify the force normal to the trajectory as the centripetal force and that parallel to the trajectory as the tangential force.