The rate of change of acceleration is the jerk and we experience that everyday when starting up our cars or braking when the lights turn red.
The rate of change of jerk, the fourth derivative of displacement with respect to time, is called the snap. Positioning spacecraft requires the calculation of snap.
Snap too may vary with time. The fifth derivative is called the crackle and the sixth derivative is called the pop but these and higher derivatives have not – yet – found practical application.
The k2p blog 