An object falling vertically, while subject to quadratic drag, will have a terminal velocity of

v*t* = sqrt[W/b],

where W is the weight of the object and b is the coefficient of the drag force.

If you apply a downward force F in addition to the weight of the object, the terminal velocity will instead be

v*t* = sqrt[(W + F)/b].

So for F > 0, the terminal velocity will be higher than the F = 0 case.