I am not sure if this question has been asked before, but I want to know, why is it the case that, in Newtonian mechanics, knowing the position and velocity of all particles at one instant is sufficient to determine the position and velocity of all particles at all other instants? Why is the acceleration and higher derivatives, like jerk, jounce, etc not necessary? I would have thought that you need to know the position and all its infinitely many iterated derivatives with respect to time to determine the state of the universe at all other instants, but why is it that you only need position and velocity?
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Possible duplicates: https://physics.stackexchange.com/q/18588/2451 and links therein. – Qmechanic Apr 09 '23 at 00:20