[Mr. K]

Actually you have to go to the third derivative for this.

Velocity is the first derivative of the change in position over time.

Acceleration is the second derivative, the change in velocity over time.

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.

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.

Thus endeth the math lesson for today that you thought you would never use from high school and college.

[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!