# Rate of Change in Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

The rate of change in acceleration ( $$a_c$$ ) 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.

### Rate of Change in acceleration Formula

$$\large{ a_c = \frac {d}{t} }$$

$$\large{ a_c = \frac { a_f \;-\; a_i }{ t }; }$$

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