Derivitives of position

Given the position of a particle or object, you can take the position over time as in the following eqn: v = (p2-p1) / t
which is one way of expressing velocity or movement.

In a similar manner, you can measure velocity over time to yield acceleration thusly: a = (v2-v1)/t

You might be surprised to learn that further derivations exist for acceleration over time and even further. These are the following (I am not making this up):
Jerk = (a2-a1)/t
Jounce = (Jerk2 - Jerk1)/t

Above that we have the following derivatives:
5th: Crackle
6th: Pop
7th: Lock
8th: Drop

These can be quite useful, particularly jerk which can be used to great effect in camera controls and animation. Once we get to Jounce, these derivatives begin to lose further value. There are some other alternatives which are less serious but still useful sometimes. Those are:

• snap - the same as jounce
• crackle - change in snap over time
• pop - change in crackle over time

In calculus terms:
v = ∆p / ∆t = dp/dt
a = ∆v / ∆t = dv/dt
k = ∆a / ∆t = da/dt (jerk)
c = ∆k / ∆t = dk/dt (jounce)

It turns out that position is the 1st derivative of absement. Absement (or absition) refers to the -1th time-derivative of displacement (or position), i.e. the integral of position over time.

Happy physics and animation