Final answer:
The student's question involves the conservation of energy on a roller coaster, where potential energy is converted to kinetic energy and vice versa as the roller coaster moves, with total energy being conserved.
Step-by-step explanation:
The student's question pertains to the conservation of energy within the context of a roller coaster's motion. According to the principle of conservation of energy, the total mechanical energy (potential plus kinetic energy) of a system remains constant if there are no non-conservative forces at play, such as friction. When the roller coaster is at the top of a rise, it has maximum potential energy due to its height. As it descends, this potential energy is converted into kinetic energy, which is at its maximum at the bottom of the descent. This interplay continues as the roller coaster moves through subsequent rises and falls, with energy shifting between potential and kinetic forms but with the total energy being conserved.
For instance, if we neglect work done by non-conservative forces, the change in potential energy (∆PEg) from moving down a distance h is equal to the gain in kinetic energy (∆KE), which can be expressed as —∆PEg = ∆KE. Since PEg = mgh and KE = ½mv², where m is mass, g is acceleration due to gravity, h is height, and v is velocity, we can solve for the final velocity at various points of the roller coaster's track.