• If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • Social distancing? Try a better way to work remotely on your online files. Dokkio, a new product from PBworks, can help your team find, organize, and collaborate on your Drive, Gmail, Dropbox, Box, and Slack files. Sign up for free.


Power - Derivation

Page history last edited by Mark Eichenlaub 2 years, 4 months ago


Power - Introduction


Now let's look at power using calculus. We know that power is the time derivative of kinetic energy


P = d/dt (KE)


so let's plug in our expression for kinetic energy,


P = d/dt (1/2 mv^2)


To take the derivative, we need to recognize a few things:

- the factor 1/2 is just a constant

- the variable m, for the mass, we will assume to be constant in this course. Because it's a constant, we don't have to worry about its derivative, it just gets carried through the calculation just like the factor 1/2 does

- v, the velocity, is a function of time. We have to use the chain rule to take the derivative. 


The result is


P = 1/2 m (2 v dv/dt)


We know another name for dv/dt - the acceleration, a. Plugging that in and combining the factors 1/2 and 2, we have


P = m v a


But here we can do another simplification. m*a is the force, F, so


P = Fv



Comments (0)

You don't have permission to comment on this page.