Consider an object that is coasting horizontally (positive x direction) subject to a drag force f = -bv - cv^2 . Write down Newton's second law for this object and solve for v by separating variables. Sketc the behaviour of v as a function of t. Explain the time dependence for t large. (Which force term is dominant when t is large?)
The Attempt at a Solution
I start with Newton's second law:
m(dv/dt) = -bv -cv^2
m(dv/dt) = -v(cv + b)
(-m/v)(dv/dt) -cv = b
dv/v + (cv/m)dt = (-b/m)dt
Then... do I integrate with respect to v for the dv terms and t for the dt terms? I can't figure out what this will give me with the second term on the right...