Calculus Project

When a roller coaster is sitting at the top of a hill the energy it possesses is called potential energy. For example, when you want to join a loop to a straight line to construct a “loop the loop”, a spline is made to connect them. They use gravity in the form of potential energy converted to kinetic energy to supply the energy needed to follow the entire track. The cycle is then repeated as the roller coaster approaches the next hill.

Concavity-a curve inward like the inside of a circle. The kinetic energy in this case reaches its max when it is at the minimum height. As the roller coaster declines from the top of the hill the energy shifts from potential to kinetic.

Second Derivative-known as the derivative of the first derivative, it is used to find the acceleration of a particle and the concavity of a curve. To fulfill this requirement, a lift mechanism drags the coaster to the top of the first hill and releases it. They do not have motors to propel them along the track. matical term used to describe, in this case, the curve that joins two functions at the nearest end points. It, ultimately, boils down to velocity control.