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## Homework Statement

A particle of mass m falls fom rest; the resistance of the air when the speed is v is kv

^{2}where k is a constant. If s is the distance fallen in time t, prove that s = V

^{2}/2g ln(V

^{2}/(V

^{2}-v

^{2})), where V

^{2}=mg/k

## Homework Equations

## The Attempt at a Solution

I have already proven that t = V/2g ln((V+v)/(V-v)). How do I make use of that equation to solve the problem? Do I have to change to v(t) equation and integrate it?