# 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.

Related Introductory Physics Homework News on Phys.org

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

Homework Helper
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.

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

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving