In terms of moving objects, the third order derivative of position as a function of time is called 'jerk', a measure of how quickly acceleration is changing with time. When I was in college, I learned to call it the surge.
From Wikipedia: "If x(t) represents the position of an object at time t, then the higher-order derivatives of x have physical interpretations. The second derivative of x is the derivative of x?(t), the velocity, and by definition this is the object's acceleration. The third derivative of x is defined to be the jerk, and the fourth derivative is defined to be the jounce."
https://en.wikipedia.org/wiki/Derivative
https://en.wikipedia.org/wiki/Jerk_%28physics%29
Obviously, if you know about this function, you would be interested in the third antiderivative in order to find the position as a function of time. The fourth derivative, which corresponds to the rate of change of jerk with respect to time, is called the jounce.
"The fourth, fifth and sixth derivatives of position as a function of time are 'sometimes somewhat facetiously' referred to as 'Snap', 'Crackle' and 'Pop'."
https://en.wikipedia.org/wiki/Jounce