If you can take an infinite number of derivatives of position, then why is it so hard to visualize/think of real world examples beyond the jerk? Does the function essentially become meaningless to the physical world?

Question

If you can take an infinite number of derivatives of position, then why is it so hard to visualize/think of real world examples beyond the jerk? Does the function essentially become meaningless to the physical world?

In: 0

Answer 1

If your position as a function of time is a polynomial at some point the derivative becomes zero.

If you integrate backwards from jerk position becomes a cubic polynomial O( x^3 ), this is sufficient for almost all uses. Sometimes [fourth, fifth, and sixth derivatives](https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position) are useful for considering vibration and shock.