Final answer:
The roller coaster at its highest point has maximum gravitational potential energy and minimal kinetic energy due to its slow speed; these energies can be calculated using PEg = mgh and KE = 1/2 mv² respectively.
Step-by-step explanation:
At the highest point of a roller coaster, the car has the maximum gravitational potential energy (PEg) because it is at the highest point in its path. Any motion it has is slow, which means it has minimal kinetic energy (KE). This is due to the conservation of energy, which states that in a closed system, such as the roller coaster and Earth, energy is conserved and merely transformed from one form to another. Most of the work done to get the coaster to the top converts to gravitational potential energy, which can be calculated using the formula PEg = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. The kinetic energy is given by KE = 1/2 mv2, where v is the velocity.
As the roller coaster starts its descent, this potential energy is converted into kinetic energy, increasing the speed of the coaster. If we neglect friction, the total mechanical energy of the roller coaster remains constant throughout the ride, assuming no additional forces do work on the system. At the top, speed and kinetic energy are at their minimum, while potential energy is at its maximum.