Final answer:
As a roller coaster ascends to the top of a hill, it gains maximum potential energy and has minimum kinetic energy. On descending, this potential energy is transferred into kinetic energy, resulting in an increase in speed. The fastest speed of the roller coaster occurs at the lowest point when potential energy is fully converted into kinetic energy.
Step-by-step explanation:
On an actual roller coaster, there are many ups and downs, which involve the transitions between kinetic energy (KE) and potential energy (PE). When a roller coaster climbs to the top of a hill, it gains potential energy due to its elevation. If we ignore any energy lost to friction, the total mechanical energy of the system remains constant, thanks to the law of conservation of energy. This concept is mathematically represented as the total energy at one point (subscript 1) being equal to the total energy at another point (subscript 2).
The roller coaster's car and its passengers accumulate a significant amount of potential energy when they are raised to the top of the first hill. This potential energy is then available to be transformed into kinetic energy or to perform work. Similarly, the gravitational potential energy that the roller coaster car possess at the top of the hill is at its maximum. At this position, the roller coaster is also moving slowly, which means it has a small amount of kinetic energy. However, as the roller coaster descends, the potential energy is converted into kinetic energy, leading to an increase in speed. The fastest speeds of the roller coaster are therefore observed at the lowest points in the ride where the potential energy has been almost entirely converted into kinetic energy.
At the top of the ramp, the roller coaster car has maximum potential energy and minimum kinetic energy. When it starts descending the hill, this potential energy is progressively converted into kinetic energy, making the car go faster. At the highest point, the car's energy is mostly in the form of gravitational potential energy, indicated by its elevated position.