system
Given the following post, respond as if you're commenting on Reddit:
human
How many derivatives can you take of a moving object before getting a value of zero?

If the position of a theoretical object was defined by x\^2, then the first derivative would be 2x, the second would be 2, and the third would be 0. How many derivatives can you take of, say, the position of a rocket ship launching into space or a person starting to run before getting a value of zero? Do some things in the universe never reach zero? Do all of them never reach zero?
gpt
It depends on how it's moving, but you can easily come up with motions where arbitrarily high time derivatives of the position will not be identically zero. An example is a simple harmonic oscillator, where the motion is described by a sinusoidal function.