A roller coaster's energy is constantly changing between potential and kinetic energy. At the top of the first lift hill (a), there is maximum potential energy because the train is as high as it gets. As the train starts down the hill, this potential energy is converted into kinetic energy -- the train speeds up. At the bottom of the hill (b), there is maximum kinetic energy and little potential energy. The kinetic energy propels the train up the second hill (c), building up the potential-energy level. As the train enters the loop-the-loop (d), it has a lot of kinetic energy and not much potential energy. The potential-energy level builds as the train speeds to the top of the loop (e), but it is soon converted back to kinetic energy as the train leaves the loop (f).
Roller coasters are driven almost entirely by basic inertial, gravitational and centripetal forces, all manipulated in the service of a great ride. Amusement parks keep upping the ante, building faster and more complex roller coasters, but the fundemental principals work just the same.
A roller coaster is like a passenger train.It has connected cars that move on tracks. However, it has no engine or power source of its own. For most of the ride it is pushed by the forces of gravity and inertia. The only time there is an exertion of energy is when the roller coaster begins its ascent.
The reason for this ascent is so it can store potential energy. The higher it is in the air, the greater distance gravity can pull it down. The potential energy that you build going up the hill can be released as kinetic energy-- the energy of motion that takes you down the hill.
Since an object tends to stay in motion, the coaster will maintain a forward velocity even when it is moving up the track, opposite the force of gravity. The course of the track is constantly converting energy from potential and back again. The changes in acceleration is what makes roller coasters so much fun.