A retarding force acts on a particle with mass m and initial velocity v0 moving on a horizontal surface; this force is proportional to the square root of the instantaneous velocity of the particle:
Fr = -k*sqrt(v)
Find an expression for the velocity of the rock as a function of time.
2. The attempt at a solution
I believe that this has to be solved through the integration of the force expression, possibly setting the right side equal to ma or m(dv/dt):
m*dv/dt = -k*sqrt(v)
dv/dt = -(k/m)*sqrt(v)
I don't know how to go about integrating this though, especially considering the v is present on both sides. I tried and this is the answer I got, though I doubt that it is correct:
v = (-3kt/m)^2 + vo
Thanks for any help!