The only time when any external force is used in a roller coaster ride is in the first lift where the roller coaster is pulled up the lift hill. This is usually accomplished with a chain lift, though in some newer models, the roller coaster is catapulted out onto the track by electromagnets.
After that, the roller coaster runs off of gravity and momentum. The roller coasters don't have brakes either. The hydraulic breaks are built into the track to stop it.