Finding velocity as a function of time

[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.

 

[Bread18]

Try inversing both sides

 

[Mmarzex]

Try inversing both sides

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

 

[Delphi51]

I know that I need to get it so that dv and v are on the same side

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.

 

[Bread18]

You inverse both sides to get dt/dv = m/(-mg - kv) and then multiply both sides by dv