Adifferential equation for the velocity v of a falling mass m subjected to air resistance proportional to the square of the instantaneous velocity is m dv dt = mg − kv2, where k > 0 is a constant of proportionality. the positive direction is downward. (a) solve the equation subject to the initial condition v(0) = v0. v(t) = (b) use the solution in part (a) to determine the limiting, or terminal, velocity of the mass. lim t→[infinity] v(t) = (c) if the distance s, measured from the point where the mass was released above ground, is related to velocity v by ds/dt = v(t), find an explicit expression for s(t) if s(0) = 0. s(t) =