A rocket in deep space starts from rest at time \(t = 0\) with an initial mass \(M_0\). The rocket engine burns fuel at a constant mass rate \(R = -\dfrac{dm}{dt}\) and expels exhaust gas at a constant speed \(u\) relative to the rocket. Assuming no external forces act on the system, which of the following expressions correctly gives the speed \(v(t)\) of the rocket as a function of time \(t\) for \(t < \dfrac{M_0}{R}\)?