After jerk come snap, crackle, and pop. These are rarely used in practice, but I believe snap (the 4th derivative) correlates with noise in high speed trains, so it's worth optimizing railroad tracks to keep snap (and of course jerk) low. This is one reason why polynomial spirals (Spiro curves) can be great tools for representing trackways or road centerlines; with G4 continuity, snap is continuous which means crackle is finite.

Also see this paper[1] (also cited by 'jjgreen elsewhere in this thread) which discusses the perception of higher derivatives in the context of roller coaster rides.

[1]: https://iopscience.iop.org/article/10.1088/0143-0807/37/6/06...