Finding velocity as a function of time

1. Feb 27, 2012

Mmarzex

Okay so the problem is that we have the case of a ball being thrown up at initial velocity v° with air resistance expressed as F = -kv where k is a constant acting on it. We are suppose to find a differential equation for the velocity at a given point as a function of time. So I started with
ƩF = ma
- mg - kv = ma

Then I moved everything around to get
dv/dt = (-mg - kv)/m

Now we have never done a solution like this in my AP Physics class so I am rather at a lose. I know that I need to get it so that dv and v are on the same side but I'm not really sure how to go about that so that I can integrate the whole equation to get the solution.

2. Feb 27, 2012

Try inversing both sides

3. Feb 27, 2012

Mmarzex

How would I find the inverse of dv/dt we have never done something like that before.

4. Feb 28, 2012

Delphi51

Take the kv term over to the other side. Multiply both sides by dt. Integrate.
You will need to remember that the integral of v*dt is distance. It works out nicely this way. I don't understand the inverse method.

5. Feb 29, 2012