Final answer:
In a system with a cyclist or a roller coaster, gravitational potential energy (PE) is maximum at the highest point and is converted to kinetic energy (KE) as the cyclist descends, reaching maximum KE at the lowest point. The process reverses during ascent.
Step-by-step explanation:
The relationship between kinetic energy (KE) and gravitational potential energy (PE) for a cyclist or on a roller coaster essentially illustrates the conversion of energy types due to gravity. When the cyclist is at the top of a rise, they have maximum gravitational potential energy and minimum kinetic energy as they are moving slowly. As they descend, their potential energy is converted into kinetic energy, resulting in increased speed and decreased potential energy. At the bottom of the descent, the kinetic energy is at its maximum because most of the gravitational potential energy has been converted into kinetic energy.
As the cyclist begins to ascend again, the process reverses: kinetic energy is converted back to potential energy, causing a decrease in speed. The principle behind these changes is the conservation of mechanical energy, assuming no energy is lost to friction or other non-conservative forces. Thus at the highest point, gravitational potential energy is at a maximum and kinetic energy at a minimum, and at the lowest point, kinetic energy is at a maximum while potential energy is at its minimum.