By the second law: F=ma
And the equilbrium law: SUM (Forces) = 0 (vec).
Okay, thus we have that when a object is falling down there are two forces: the force of gravity and the resistance force. By the conditions of the problem the resistance force is proportional to the square of speed, in simple terms, kv^2. But! There is also a downard force, w, the weight. Since the sum of the forces is zero, we have,
w-kv^2=0 (since it is going in opposite direction, thus we have a negative).
By Newton's second law the overall force is: a(w-kv^2) where "a" is acceleration. The acceleration in this case is the constant at g. Thus,
But there is another way to find the force.
Again, F=a*m=(dv/dt)*w because m, mass, and weight are presumably the same here. And dv/dt is the acceleration, as you know.