# Modeling with Differential Equations

1. Jan 21, 2013

### aaronfue

1. The problem statement, all variables and given/known data

A falling body of mass m, encounters air resistance proportional to its instantaneous velocity, v. Use Newton's second law to find the DE for the velocity, v at time, t.

2. Relevant equations
I've been reading this section quite a bit and am still not getting it! I'd appreciate a simple breakdown of this problem.

3. The attempt at a solution

I know Newton's second law is F=ma, and a=$\frac{dv}{dt}$= -g, in this problem. I've checked the answer in the back of the book to see if I can work it backwards and then maybe get an idea of whats going on, but I don't think I've dealt with air resistance, k, in any problems before. Even in my physics class.

2. Jan 21, 2013

### SammyS

Staff Emeritus
Newton's 2nd Law: The net force on a body of mass, m, is given by Fnet = ma .

For this problem Fnet = mg - kv , and is in the downward direction.

3. Jan 22, 2013

### aaronfue

I see. There was an image next to the question with those being opposite. Now to put ity into a differential equation form? I was watching a video about differential equations and there being a 1st ODE format using p(x) and q(x)?

4. Jan 22, 2013

### haruspex

What differential equation relates acceleration to velocity?