# Velocity Drag force and distance traveled

1. Sep 13, 2016

### nysnacc

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

2. Relevant equations
Sum of force

a = dv/dt
v = integrate a + C

3. The attempt at a solution

I found the equation in terms of final v, initial v... however, on the right hand side, there is another v, and I think it is time dependent, so I am not sure which value should I plug in.

2. Sep 13, 2016

### TSny

Try using the chain rule to write $a = \frac{dv}{dt} = \frac{dv}{dx} \frac{dx}{dt}$.

3. Sep 13, 2016

### nysnacc

Then do we know dv/dx and dx/dt? on the right hand side, will the velocity be initial one? thanks

4. Sep 13, 2016

### TSny

Try to express F = ma as a differential equation in terms of just the variables v and x. dv/dx is already expressed in these variables. How can you express dx/dt?

v on the right side of a = F/m is the instantaneous velocity.

5. Sep 13, 2016

### nysnacc

so dv/dx * dx/dt = -40/m v^2 ??

6. Sep 13, 2016

### TSny

Yes. In order to get only the variables v and x to appear in the equation, what can you do with dx/dt?