A research rocket of initial mass \(M_0\) is launched vertically upward from rest at time \(t = 0\) near Earth's surface in a uniform gravitational field of magnitude \(g\). The rocket engine produces a constant upward thrust force of magnitude \(F_0\) while consuming fuel at a constant mass rate \(b\), so that the total mass of the rocket varies with time according to \(m(t) = M_0 - bt\). Air resistance is negligible, and \(F_0 > M_0 g\). Which of the following expressions represents the upward speed \(v(t)\) of the rocket as a function of time for \(0 \le t < M_0/b\)?