(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I recently finished a test that asks you to derive

[itex]Power = \frac{dE}{dt} = F \times v[/itex]

from the energy equation:

[itex]E^2 = E_{0}^2 + (pc)^2[/itex]

2. Relevant equations

[itex]Power = \frac{dE}{dt} = F \times v[/itex]

[itex]E^2 = E_{0}^2 + (pc)^2[/itex]

[itex]p = \gamma m v[/itex]

3. The attempt at a solution

I got there in kind of a messy way but I would like to know how I could have more cleanly shown how to put it together. Here's the way I got to it:

[itex]2E \frac{dE}{dt} = 0 + 2pc \frac{dp}{dt}[/itex]

[itex]2(\gamma mc^2) \frac{dE}{dt} = 0 + 2 \gamma mvc \frac{dp}{dt}[/itex]

[itex]\frac{dp}{dt} = F \stackrel{and\rightarrow}{} \frac{dx}{dt} = v [/itex]

therefore [itex]\frac{dE}{dt} = P = Fv[/itex]

Of course, I also realize I may have bungled this, so corrections or at least references to the rules would also be much appreciated. Please, weigh in.

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# Homework Help: Deriving power from the relativistic energy equation

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