Deriving velocty with drag equation

[M4573R]

Homework Statement

Derive an equation for velocity based on time with drag.

Homework Equations

The equation is: v(t) = F/b (1 - e^(-bt/m))

The Attempt at a Solution

There's some math on paper, but I got down to:
F - bv = ma
a = dv / dt

F - bv = m*dv/dt

dt = m*dv / (F - bv)
integrate both sides

t = m*(-ln(|bv-F|) / b)

-tb/m = ln(|bv-F|)

e^(-tb/m) = |bv-F|

here is where I don't know how to simplify it anymore. What do I do with the absolute value?
If I ignore it, it doesn't simplify right, or at least I can't get it to.

 

[alphysicist]

Hi M4573R,

Homework Statement

Derive an equation for velocity based on time with drag.

Homework Equations

The equation is: v(t) = F/b (1 - e^(-bt/m))

The Attempt at a Solution

There's some math on paper, but I got down to:
F - bv = ma
a = dv / dt

F - bv = m*dv/dt

dt = m*dv / (F - bv)
integrate both sides

t = m*(-ln(|bv-F|) / b)

This equation is not right. These are definite integrals, so you need to evaluate them at the limits. Evaluate the right hand side for an initial speed of zero and for the final speed v and then solve for v. Do you get the result they ask for?



About the absolute value: with the equation you are looking for, you know that F cannot be smaller than bv, so what does $|bv-F|$ equal?