You can get (a) by using the given differential equation and solving for t.
Since are constants, you have equal to a function of t, so you only have to take the integral of both sides to get s as a function of t.
If you don't know how to integrate, try setting , take the derivative and choose values of to make the equation work. You'll have to use the initial condition s(0)=0 to get C.
The answer to (c) is that the question is invalid - if you look at the differential equation, you see that never reaches zero, so it never stops. But you can take the limit as t goes to infinity of the equation you found in (b) to get the result.
Post again in this thread if you're still having trouble.