Final answer:
Potential and kinetic energy commonly have an inverse relationship in a conserved system, where potential energy is converted to kinetic energy and vice versa. However, kinetic energy itself is directly proportional to the square of the velocity.
Step-by-step explanation:
The relationship between potential and kinetic energy is that they can be inversely related in systems where the total mechanical energy is conserved. When an object is at a height, it has potential energy due to its position, but as it falls, this potential energy is converted to kinetic energy, which depends on the object's mass and velocity as given by the equation KE = 1/2mv². This illustrates an inverse relationship, as the increase in kinetic energy comes at the expense of potential energy and vice versa.
However, it's also important to note that the equation cited from the question suggests a different context in which kinetic energy is directly proportional to the square of the velocity, not an inverse relationship. This implies that when an object's velocity increases, its kinetic energy increases exponentially (since the velocity is squared in the kinetic energy formula). This statement reflects a direct relationship between the velocity component of kinetic energy and the kinetic energy itself. Although this seems to contradict the previously mentioned inverse relationship, it's crucial to understand that the relationships mentioned refer to different aspects of energy transformations.
Therefore, the most accurate answer to the student's question would be that potential and kinetic energy have an inverse relationship in the context of a trade-off within a conserved system, but kinetic energy has a direct relationship with the square of velocity in terms of how it is calculated.