Final answer:
As a wagon accelerates down a hill, potential energy decreases due to a loss in height, while kinetic energy increases as the wagon's speed increases. At the hill's bottom, potential energy is at its minimum and kinetic energy is at its maximum.
Step-by-step explanation:
When discussing the situation where a wagon accelerates down a hill, the concepts of potential energy and kinetic energy are key to understanding the energy transformations that occur. Potential energy decreases as the wagon moves down the hill because it is losing height, which is directly proportional to its gravitational potential energy. Simultaneously, the kinetic energy increases because the wagon is gaining speed as it descends due to the acceleration caused by gravity. At the bottom of the hill, the potential energy is at its minimum because the elevation is lowest, while kinetic energy is at its maximum because the velocity is greatest.
The example of a child swinging also illustrates these principles. As the child swings downward, gravity is aiding in the child's acceleration, thereby increasing kinetic energy. Conversely, as the child swings upward, they are moving against gravity, which results in an increase in potential energy and a decrease in kinetic energy since they are slowing down.
It's important to remember that in these scenarios, energy is conserved. The decrease in potential energy is balanced by an increase in kinetic energy, and vice versa, minus any energy that might be lost due to non-conservative forces like friction.