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## Homework Statement

A metal block of mass m slides on a horizontal surface that has been lubricated

with a heavy oil so that the block suffers a viscous resistance that varies as the 3/2

power of the speed: F(v) = -cv

^{3/2}

If the initial speed of the block is v

_{o}at x = 0, show that the block cannot travel farther than 2mv

_{o}

^{1/2}/c

## Homework Equations

F = ma = m[itex]\frac{dv}{dt}[/itex]

## The Attempt at a Solution

So, I took

m[itex]\frac{dv}{dt}[/itex] = -cv

^{3/2}

I rearranged it and got

dv/v

^{3/2}= [itex]\frac{-c}{m}[/itex]dt

I've tried integrating this and I can't seem to end up with the right answer. I'm totally lost. Anyone have any ideas?

EDIT: No help at all?

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