I’ve elaborated some, in the hopes of clarifying, but here is the gist of the students’ question:
When you throw a ball up in the air, we know it loses kinetic energy, because it’s obviously slowing down. We also know we can describe that loss of kinetic energy in terms of the work being done on the ball due to the gravitational force from earth. But what about the rate at which energy is being lost? Since we also know we can determine the rate at which energy leaves the ball by considering the quantity F.v. , then we can say when the ball is moving fast it loses energy quickly, and when the ball is moving slowly it loses energy slowly. This also makes sense from a potential energy perspective, because when you are moving fast you cover more distance, so the potential energy term mgh also changes quickly. But right at the top, when the ball is not moving, it has zero kinetic energy; but also the rate at which energy is being transferred to / from the ball is zero.
Question: How does the ball go from having no kinetic energy to having some kinetic energy a moment later? Think about it. For the ball to have kinetic energy, it has to be moving; but for it to get moving there needs to be a flow of energy; but for there to be a flow of energy, it needs to be moving already.