# Rate of Change in Acceleration

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 |