You have the most potential energy at the top of a hill. Where would you have the most kinetic energy?
- I was thinking right before you stop rolling down the hill
"At the bottom" is the answer. You don't stop rolling there; you roll fastest there.
To determine where you would have the most kinetic energy, we need to understand the relationship between potential energy and kinetic energy.
Potential energy is the energy possessed by an object due to its position or arrangement. In the case of being at the top of a hill, an object has the highest potential energy because it is furthest from the reference point (usually the ground) and hence has the greatest potential to do work as it moves downward.
On the other hand, kinetic energy is the energy possessed by an object due to its motion. It is defined as ½ times the mass of the object multiplied by the square of its velocity.
As you start rolling down the hill, your potential energy decreases, and your kinetic energy increases. At any point during the descent, both potential and kinetic energy are present, but their values change.
The point where you would have the most kinetic energy is at the bottom of the hill, right before you stop rolling. At this point, your potential energy is almost zero because you are closest to the reference point (the ground). Since potential and kinetic energy are interconvertible, nearly all the initial potential energy you had at the top of the hill is transformed into kinetic energy as you reach the bottom and come to a stop.
In summary, while potential energy is greatest at the top of the hill, the most kinetic energy is acquired right before you stop rolling down the hill at the bottom.