# Integrating to determine speed as a function of time

1. Oct 24, 2012

### AryRezvani

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

2. Relevant equations

The above formulas

3. The attempt at a solution

I'm lost on where to start with this. The object has an intial velocity in the X direction and has the resistive force of the plontons acting upon it when it lands. What exactly is the equation located in the problem?

2. Oct 24, 2012

### tiny-tim

Hi AryRezvani!
That's good ol' Newton's second law, F = ma

F = -bv, ma = mdv/dt, so mdv/dt = bv, so dv/v = -b/m dt

(the "m =" appears to be a misprint)

3. Oct 24, 2012

### AryRezvani

Thanks for the response Tiny-Tim :)

Okay, so i follow you somewhat. F = -bv (general formula for resistive force).

According to Newton's second law, F=ma which can be rewritten as F=m(dv/dt).

You then equate those two, and you get m(dv/dt)=-bv.

What happens after this? (dv/v) is the derivative of velocity with respect to velocity?

4. Oct 24, 2012

### tiny-tim

ah, no …

∫ dv/v is a short way of writing ∫ (1/v) dv …

just integrate it!

5. Oct 24, 2012

### AryRezvani

Ohh so when you integrate that you get ln(v)?

6. Oct 24, 2012

### tiny-tim

yes!

(to be precise, ln(v) - ln(vo))