>>11652652You're sort of thinking about this wrong...
Clasically, force is proporitonal to acceleration, which is the second derivative of position wrt time. It is currently believed that there are four fundamental forces - Gravitational, Strong, Weak, Electromagnetic (and that at high energies all these forces are the same but they separate at lower energies due to symmetry breaking, but that's beyond the scope of the question), and that these four forces (especially electromagnetism) are responsible for all the macroscopic forces which arise from the complex interactions of many particles and forces (for example, friction).
We have yet to find motion which isn't adequately described by forces - However, it's more than possible for the magnitude of a force to be dependent on the velocity of an object, which is a common model for friction in oscillating systems. It's similarly possible to dream up forces, fundamental or macroscopic, whose magnitude depends on higher order derivatives, such as the jerk, snap, crackle, pop, etc.
But those are of course merely speculative problems, which may or may not point towards interesting physical phenomena. More to the point, "do the derivatives go on forever or does it become meaningless?" is sort of a malformed question. Anybody who has watched a sport knows that human bodies, among other objects, do not accelerate at uniform rates - the forces being applied are constantly changing as the mind assesses a situation and reacts, changing the acceleration, and changing the rates at which the acceleration is changing (the jerk). A complicated enough trajectory, such as that produced by a footballer maneuvering around an opponent, will almost certainly have nonzero time derivatives to a very high order. The same could be true of any mechanical system, receiving human input or just undergoing very complex interactions with its environment.
