Energy consumed by variable drag force when stopping?

[charlie988]

I was trying to roughly calculate the energy that could be recovered by regenerative breaking when bringing a vehicle to a stop, so I calculated to total kinetic energy and then tried to calculate the work done by air resistance that would take away from the energy that could be captured. So I calculated the drag force equation as F = 2.826 x v^2. Therefore, work would equal the the Integral of (2.826 x v^2)dx. But, this can't be integrated, as velocity is a separate variable than distance.

I'm not sure how to get around this to get the work calculation, but any help or suggestions would be greatly appreciated. Thanks.

 

[Dr. Courtney]

You need to express velocity as a function of position.

Alternatively, you can express velocity as a function of time and rewrite the integral in terms of time.

 

[tommyxu3]

That is, you need to get the relation between $F$ and $x$ from $f=2.826v^2$ first, or $m\frac{dv}{dt}=2.826v^2.$