[Svartalfiar]

But if you were to immediately accelerate from zero To maximum velocity (Constant acceleration) It would probably snap your neck.

So the acceleration is actually Changing over time (third derivative) from zero to max acceleration.

Correct, and for most physics problems, this factor is mostly ignored. Force is assumed to be constant, so the acceleration is treated as near-instantaneous. Of course it really isn't, but for a practical math perspective, it is.


I once had to implement a pretty cool math algorithm for changing the acceleration of a large factory cutting table.
If you didn’t ramp-up the acceleration slowly it would jolt the machine back and forth like crazy.

Yup. Jerk is the change in acceleration, and snap is the change in jerk. Dunno if you got that far into your maths, but jerk definitely would have been involved there!

[Mr. K]

It was pretty cool watching the math implemented in real life.

We even had to measure and take into consideration the natural frequency of various components.