Something I've been wondering for awhile about this: is it specifically jerk that humans can't handle well, or all of the higher order derivatives? A lot of times we're talking about a car that's at rest (and has been at rest for delta t>0), so every order derivative is going to be positive when the value starts increasing (the rate of increase, the rate of rate of increase, the rate of ...).

Is there something specific about jerk that makes it important to optimize for, or are all position derivatives of order 3+ the same?

A mental model I employ is: from a frequency response perspective, humans are 30Hz high pass filters. That means we end up conducting more high-frequency force (either by actively fighting it or by having it act against our inertia by transmitting thru our bodies), and this is work. In the lower frequencies, we can generally more actively participate and e.g. spread out the energy transfer over longer time periods to decrease instantaneous forces in joints/etc. Picture jumping off a 3 ft ledge, you can "eat" most of the impact with your legs bending, but some of the energy is going to affect you. The mental model is that it's the high-frequency content that human bodies don't handle well.

> Is there something specific about jerk that makes it important to optimize for, or are all position derivatives of order 3+ the same?

I think of it in terms of neck muscles. If your car is accelerating at a constant rate, you feel that as a force pushing your head back. Your neck muscles activate to compensate and keep your head still.

If the acceleration changes suddenly and aggressively (i.e. high jerk), so does the force on your neck. So either your neck muscles react quickly to counteract the new force, or your head bounces around.

Higher order derivatives also matter, but mostly inasfar as they act on the acceleration (and hence force) that you feel.