Calculating Drag Force on Boat: Speed as Function of Time

[datapirate42]

F = -kv²

A fishing boat of mass m moves through the water in the +x direction. At time = 0 and x=0 it shuts its engines off and begins to drift. It experiences drag according to the above equation, calculate the boat's speed as a function of time.

I've tried taking F = ma
so a = -kv²/m

now v should be the integral of that with respect to time
my problem is getting v as a function of t without it being in that function itself

 

[Doc Al]

Hint: Replace a with its equivalent dv/dt.