A rocket has total mass Mi=360 kg, including Mf=330 kg of fuel and oxidizer, In interstellar space, it starts from rest at the position x=0, turns on its engine at time t=0, and puts out exhaust with relative speed ve=1500 m/s at the constant rate k=2.50 kg/s. The fuel will last for a burn time of Tb=Mf/k=330 kg/(2.5 kg/s)=132 s. Show that during the burn the velocity of the rocket as a function of time is given by
