Velocity Drag force and distance traveled

[nysnacc]

Homework Statement

Homework Equations

Sum of force

a = dv/dt
v = integrate a + C

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.

 

[TSny]

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

 

[nysnacc]

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

 

[TSny]

Then do we know dv/dx and dx/dt?

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?

on the right hand side, will the velocity be initial one? thanks

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

 

[nysnacc]

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

 

[TSny]

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

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