Is there a word describing the derivatives of an object's motion?

Question

Consider an object moving along a straight line. One might say something about its displacement, velocity or acceleration. These are the 0th, 1st and 2nd derivatives of the object's displacement. However, there are an infinite number of derivatives although we may rarely talk about the 1001st derivative.

Is there a name for the infinite set: {0th derivative of displacement, 1st derivative of displacement, 2st derivative of displacement, ......... }?

I've come across the problem of trying to describe this set in writing a mathematical piece of work related to the Maclaurin/Taylor series.

So far, I describe it as "derivatives of the object's motion" although I'm not too sure if this is quite right.

Answer 1

Here is a common convention for position derivatives

• 0^th Derivative : Position
• 1^st Derivative : Speed
• 2^nd Derivative : Acceleration
• 3^rd Derivative : Jerk ^[1]
• 4^th Derivative : Snap/Jounce ^[2]
• 5^th Derivative : Crackle
• 6^th Derivative : Pop
• 7^th Derivative : Lock ^[3]
• 8^th Derivative : Drop
• 9th Derivative : ???

Beyond that, it is just an academic exercise in naming as it way beyond any practical use.

Footnotes

1. Names of higher-order derivatives
2. https://en.wikipedia.org/wiki/Jounce
3. https://www.researchgate.net/post/What_are_the_physical_names_for_third_fourth_and_higher_order_derivatives_of_position