Show that for a single particle with constant mass the equation of motion implies the following differential equation for the kinetic energy:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]{dT\over dt} = \vec F \cdot \vec v[/tex]

while if the mass varies with time the corresponding equation is

[tex]{d(mT)\over dt} = \vec F \cdot \vec p[/tex]

Proof:

I was able to prove the first part:

[tex]T = {1\over 2}mv^2[/tex]

[tex]{dT\over dt} = {1\over 2} {d(mv^2)\over dt} = \vec v \cdot m{d\vec v \over dt} = \vec F \cdot \vec v[/tex]

But I am unable to prove the second part. Please help.

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# Homework Help: Force and energy proofs

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