Question

lets consider a scenario of a roller coaster ride. as the roller coaster at the top begins to descend, it loses height, which means its potential energy decreases and kinetic energy starts increasing and reaches its maximum value. by using the above scenario, which statement best compares potential and kinetic energy? objects always have more potential energy than kinetic energy. kinetic energy increases and potential energy decreases when the velocity of an object increases. only potential energy decreases when an objects height increases. objects always have more kinetic energy than potential energy.

Explanation:

Step1: Analyze each option

• Option 1: Objects always have more potential energy than kinetic energy. This is not always true. For example, at the bottom of the roller - coaster (when height is minimum), kinetic energy is maximum and potential energy is minimum. So this option is incorrect.
• Option 2: Kinetic energy increases and potential energy decreases when the velocity of an object increases. When the roller - coaster descends, its height \(h\) decreases. The potential energy formula is \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity and \(h\) is height). As \(h\) decreases, \(U\) decreases. The kinetic energy formula is \(K=\frac{1}{2}mv^{2}\). As the roller - coaster descends, its velocity \(v\) increases (due to the conversion of potential energy to kinetic energy), so \(K\) increases.
• Option 3: Only potential energy decreases when an object's height increases. When an object's height increases, potential energy \(U = mgh\) increases (if \(m\) and \(g\) are constant) and if the object is also decelerating (while going up), its kinetic energy \(K=\frac{1}{2}mv^{2}\) decreases. So this option is incorrect.
• Option 4: Objects always have more kinetic energy than potential energy. This is not always true. For example, at the top of the roller - coaster (when velocity is minimum), potential energy is maximum and kinetic energy is minimum. So this option is incorrect.

Answer:

Kinetic energy increases and potential energy decreases when the velocity of an object increases.