Please let me ask a theoretical question. According to derivative definition, in accelerating motion (first) derivative at moment t1 is the limit of the function (constructed from position's function) for variable's limit t1. Then is it axiom that this function's limit is the speed at t1? Regards.
closed as unclear what you're asking by Cameron Williams, Hans Lundmark, Mauro ALLEGRANZA, Shailesh, Brian Borchers Apr 13 '18 at 14:09
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I think you are mixing up, somehow, axioms, and definitions.
On an other hand, you are also mixing the real world and the/a mathematical representation of the real world.
We Define Speed function as being the derivative of the Motion function, taken into consideration that we suppose, by default, in Newtownian mechanics, that the Motion function can always be derived, by the way it is defined...
In an other framework of representation of the real world, for instance Quantum Physics, such notion as Motion and Speed are not defined the same way, and it becomes more difficult to go from one to the other...