# Rate of Change in Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

The rate of change in acceleration, abbreviated as $$a_c$$, is the time derivative of acceleration, the second derivative of velocity or the third derivative of position.  In physics, it is known as the jerk.

 $$\large{ a_c = \frac {d}{t} }$$ $$\large{ a_c = \frac { a_f \;-\; a_i }{ t } }$$ Where: $$\large{ a_c }$$ = rate of change in acceleration $$\large{ d }$$ = displacement $$\large{ a_f }$$ = final acceleration $$\large{ a_i }$$ = initial acceleration $$\large{ t }$$ = time taken for change in velocity