A model rocket cart of initial mass \( M_0 \) rests on a straight, horizontal, frictionless track. At time \( t = 0 \), the rocket engine ignites and ejects gas backwards at a constant rate \( R \) (where \( R = \dfrac{dm_{gas}}{dt} \)). The gas is ejected with a constant speed \( v_e \) relative to the rocket cart. The engine operates until a total mass \( M_g \) of gas has been ejected.