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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The first reason is theoretical. For some unknown reasons, our physical laws run on the relationship between position and velocity. This means that any higher derivatives don’t provide additional information. You can use one extra level of derivative to make convenient computation, but this usefulness rapidly decrease the more derivatives you use. That’s why you basically don’t even see much beyond acceleration.
The second reason is practical. We don’t get an infinite amount of data, or perfect data without error. Small errors get amplified the more errors you have, and the less data you have, and the more derivative you have. So too many derivatives produces data that are basically indistinguishable from noises.
The third reason is that a position function is an *idealized* version of the real world’s position. Objects don’t actually have specific pinpoint positions for many reasons, and what we assigned to be its position function is just an approximation. This makes infinite many derivatives not that useful.
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