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## Homework Statement

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!

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