Hello, Something on my mind today... As you keep differentiating functions that are sometimes used to represent the displacement of objects you eventually end up with a function that has discontinuities and jumps in its path. Simple example for the sake of illustration - an object at rest starts accelerating at 1 m/s^2 at t=0. f(x) = 0, for x [itex]\leq[/itex] 0 f(x) = x^2, for x>0 f'(x) = 0, for x [itex]\leq[/itex] 0 f'(x) = x, for x>0 f''(x) = 0, for x [itex]\leq[/itex] 0 f''(x) = 1, for x>0 How are these jumps and discontinuities dealt with a real-world physical sense ? A jump in position would infer instantaneous/greater than light speed travel, but why is there no issue for acceleration ? I read about jerk and jounce and so on (the 4th and 5th derivatives), but what are the rules and mechanisms for when and how each derivative is 'allowed' to make these instantaneous changes in value ? Maybe there was an infinite regression of them - an infinite derivative maybe and there was some kind of mathy limit involved ? Maybe I'm looking at simplified math text book examples/models (polynomials) and reading too much into them and the real world physical equations account for my conundrum ? Is t=0 the big bang ? and everything is in deterministic sense always moving already and these jumps don't exist ?