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Offline Medeek

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Physics Questions
« on: May 17, 2019, 05:27:14 am »
Has anyone else ever wondered where the 1/2 comes from in the equation for the kinetic energy of an object (E=1/2mv^2)? It finally donned on me why, I probably could have realized why years ago but I never really thought about it until now.
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Nathaniel P. Wilkerson, P.E.

Offline Medeek

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Re: Physics Questions
« Reply #1 on: May 17, 2019, 05:29:35 am »
The short answer is that it has to do with the integration of the momentum term in the derivation of the kinetic energy.

The more formal answer is:





Strangely enough I only thought about this while I was reading on a completely different topic and noticed that the equation given for the potential energy stored in a spring is E = 1/2kx^2. I occurred to me that this expression looked surprisingly similar to the expression for kinetic energy. It all became clear to me when I realized that the momentum is a linear function of the velocity (p=mv) as is the force a linear function of the displacement (F=kx).
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Nathaniel P. Wilkerson, P.E.
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