Physical meaning and significance of third derivative of a function

Question

Given a physical quantity represented by a function $f(t,x)$ what is (if there is any) the actual meaning of the third derivative of $f$, $\frac{\partial^3 f}{\partial t^3}$ or $\frac{\partial^3 f}{\partial x^3}$

Answer 1

Yeah it's a physical quantity known as jerk. It is as you might think the rate of change of acceleration.

For more info, see this https://en.wikipedia.org/wiki/Jerk_(physics).

Answer 2

This physical quantity is called as Jerk which is by definition the rate of change of acceleration. $$\vec{j}(t)=\dfrac{\mathrm d\vec{a}(t)}{\mathrm dt}=\dfrac{\mathrm d^2\vec{v}(t)}{\mathrm dt^2}=\dfrac{\mathrm d^3\vec{x}(t)}{\mathrm dt^3}$$

As an everyday example, driving in a car can show effects of acceleration and jerk. More skilled and experienced drivers can accelerate smoothly, but beginners often provide a jerky ride.