Gravity is the driving force of a roller coaster. From the moment the roller coaster train passes the peak of the lift hill, it is the acceleration due to gravity that brings it back to the beginning. When the train is released from the top of the lift hill, gravity pulls it down. The train begins slowly, then picks up speed as it approaches the bottom of the hill. As it begins to climb the next hill, the speed decreases. This is because of the acceleration due to gravity, which occurs at 9.80m/s2 straight down toward the center of the Earth.
The initial hill, or the lift hill, is the tallest in the entire ride. As the train is pulled to the top, it is gaining potential, or stored energy. The higher the lift, the greater the amount of potential energy gained by the train. This is shown by the equation for potential energy:
Ug = mgh
Where Ug is potential energy, m is mass in kilograms, g is acceleration due to gravity, and h is the distance above the ground in meters. Because mass and gravity are constant for the train, if the height of the train above the ground is increased, the potential energy must also increase. This means that the potential energy for the roller coaster system is greatest at the highest point on the track: the top of the lift hill.