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.

 

rate of change in acceleration formulas
\(\large{ a_c = \frac {d}{t}  }\)  \(\large{ a_c = \frac { a_f \;-\; a_i }{ t } }\)
Symbol	English	Metric
\(\large{ a_c }\) = rate of change in acceleration	\(\large{\frac{ft}{sec^3}}\)	\(\large{\frac{m}{s^3}}\)
\(\large{ d }\) = displacement	\(\large{ ft }\)	\(\large{ m }\)
\(\large{ a_f }\) = final acceleration	\(\large{\frac{ft}{sec^2}}\)	\(\large{\frac{m}{s^2}}\)
\(\large{ a_i }\) = initial acceleration	\(\large{\frac{ft}{sec^2}}\)	\(\large{\frac{m}{s^2}}\)
\(\large{ t }\) = time taken for change in velocity	\(\large{ sec }\)	\(\large{ s }\)