# Energy consumed by variable drag force when stopping?

1. Jul 14, 2015

### 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.

2. Jul 14, 2015

### 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.

3. Jul 14, 2015

### tommyxu3

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