If you can take an infinite number of derivatives of position, then why is it so hard to visualize/think of real world examples beyond the jerk? Does the function essentially become meaningless to the physical world?
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In an attempt to actually answer the question in a proper ELI5 manner:
*So much* of the motion we see around us does actually have 4th/5th/6th/whatever derivatives of position, but ignoring it rarely matters – the difference is usually small or takes a long time to add up to something large.
Our ability to see the world is *heavily* influenced by what is useful for passing on our genes – instinctive 5th differentials don’t really help you run away from a tiger or find berries, so evolution hasn’t provided that ability.
Similarly, even though it’s something a suitably smart person probably could learn, that would require experiences where it matters and effort to understand its effects, and *you* don’t find it important enough to have worked on that ability, either.
Because of all this, we don’t have an intuitive (or trained) grasp of how the Nth derivative *looks* or *feels* so we don’t see it, even when it’s under our noses (or under the seat of our pants as our car trundles over rough surfaces – see the [J-damper](https://www.formula1-dictionary.net/j-damper.html) I mentioned in another post).
I’d bet you a shiny penny that the 4th/5th/Nth derivatives of the motion of a leaf fluttering in a stiff breeze aren’t zero until you get up to a pretty high number, but who cares? Certainly not your genes, and probably not you, either, really…
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