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Physics/Instantaneous velocity

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Question
Hello,
Concerning the concept of instantaneous velocity, for example when the velocity of a body moving in a simple harmonic motion reaches zero at the maxiumum displacement from the equilibrium position does it come to rest for zero time or for infinitesmally short time?
and is there a mathematical proof for your answer ?
Thanks in advance

Answer
Well, it's "infinitesimally short," which is essentially zero.  Your question results in a fundamental problem for physics, as we have not been able to probe whether or not the Planck time is the shortest possible unit of time and have no chance to do so experimentally.  They're practically equivalent, but there's no good way to mathematically answer your question.

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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