I read that the rate of change of acceleration is called Jerk, and the rate of change of Jerk is called Jounce. I guess sometimes these higher order derivatives are used when designing extremely precise equipment, like the Hubble or someone on this form said camshaft design. We can even talk about higher order derivatives of Jounce, but I can see how these would not be useful in most situations. In the real world there is probably no such thing is perfectly constant acceleration, jerk, jounce, snap, crackle, and pop. Could you just keep taking higher order derivatives forever to describe motion? Is this just the same thing as asking what is the smallest possible delta t?