Potential and kinetic energy are the two types of mechanical energy. An object stores potential energy and expends it as kinetic energy when it is in motion. Potential energy generally involves an object's potential for movement as a result of its place within the gravitational field of the Earth.
When a roller coaster travels up the first hill at the beginning of the ride, it is building potential energy. It also shows kinetic energy, as it is rolling up the hill, but the gravitational effect of going uphill is one factor causing the roller coaster to slow down. The kinetic energy is converting to potential energy because the higher the roller coaster goes, the faster it is able to go once it reaches the top of the slope.
Once the roller coaster comes over the top and heads down the hill, the potential energy drops in a hurry, converting into kinetic energy. Calculating potential energy at any point with respect to gravity follows this formula: PE = m * g * h, where m is an object's mass in kilograms, g is the acceleration that gravity produces and h is the object's height in meters. Calculating kinetic energy uses this formula: KE = 0.5 * m * v^2, where m is the mass of the object in kilograms and v is the velocity of the object in meters per second.