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How has it been proven that the derivative of position is velocity and the derivative of velocity is acceleration? From Google searching, it seems that everyone just states it as fact without any proof behind it.

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    It's a definition, not a proof.2012-12-16
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    There's no such thing as definition without a proof in mathematics. Everything can be proved somehow and I'm also looking for an analitic answer to the question, the conceptial one (given by @Jasper Loy) can be reached by drawing a graph and letting the brain figure it out.2013-03-17
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    @MarcoAurélioDeleu That's complete nonsense. *Proofs* are needed to justify logical statements, but definitions aren't logical statements. Definitions aren't true or false or provable or unprovable. Definitions allow us to make shorthands for bundles of hypotheses (for instance, the definition of a circle in geometry.) You can't *prove* the definition of a circle.2013-09-30
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    It does not need proof. I could say "let the amount of tinned food you buy per week be called Tintin!" That does not need a proof of any sort does it. It is just a definition / statement to allow us to use it in speech, calculations, etc. In terms of derivatives, after velocity there is acceleration, jerk, jounce, crackle, pop,... The derivative list is endless.2014-07-04
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    Possibly of interest: [What does the integral of position with respect to time mean?](https://math.stackexchange.com/questions/1637409)2017-07-21

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