"Accelerations" as higher order derivatives

[E Rinella]

TL;DR Summary

Physical interpretations of higher order derivatives of time: velocity, acceleration, etc. ...

In physics, velocity (speed) is the "change of position (spacial location) per change of time" and acceleration is the "change of velocity per change of time". Mathematically this is first and second derivative. Do further derivatives exist that correspont physical quantities like "change of acceleration per change of time" ... etc.?

 

[Baluncore]

Yes.
Position, Velocity (speed), Acceleration, Jerk, Snap (jounce), Crackle, Pop.
https://en.wikipedia.org/wiki/Jerk_(physics)