Newtonian mechanics - mass of rocket

A rocket having initial mass *m*_{0} kg is launched vertically from the ground. the rocket expels gas at a constant rate of *a* kg/s and at a constant velocity *b* m/s relative to the rocket. Assuming that air resistance is proportional to the rocket velocity *v(t)* with prop. constant *k*, find the velocity of the rocket at t=6s, and after the mass *m*_{g} kg of gas is used up.

Solution:

Let M be mass at any time t

M(t)' = -(at^{2})/2 + c

Solving gives M = m_{0 }- (at^{2})/2

After this I'm not sure how to use the forces. Can someone help with the next steps please? Thanks.