A repair satellite of mass \(m\) is traveling through deep space with a constant speed of \(3v_0\). It undergoes a docking sequence with a stationary telescope of mass \(2m\). The docking mechanism causes the two objects to stick together and move as a single unit immediately after impact. Once docked, a reverse thruster on the satellite is activated, providing a constant braking force of magnitude \(F\) in the direction opposite the motion. In terms of \(m, v_0\), and \(F\), what is the total distance the system travels while the thruster is active before coming to a complete stop?