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## Homework Statement

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

^{2}where k is a constant. Show that after a time t, the velocity v and the time t are related by the equation t = V/2g ln[(V + v )/(V - v)] where V

^{2}

= mg/k

## Homework Equations

## The Attempt at a Solution

ma = mg - kv

^{2}

a = g - k/m v

^{2}

dv/dt = g - k/m v

^{2}

dv = g - k/m v

^{2}dt

v = gt - k/m v

^{2}t

t = v/(g - k/m v

^{2})

But I don't know how to continue from here.

I have been studying differential equation on my own, so I am not very strong in the foundation