Question

The change in kinetic energy is always ______________ to the change in potential energy.

Answer 1

Do you have any guesses?

(I assume we're going to say mechanical energy is conserved, for this question.)

Answer 2

So, we assume, as @theEric said, that energy is conserved. We also have the following equation:\[E _{total}=KE+PE\]where E is the total energy--and in this case a constant; KE is kinetic energy; and PE is potential energy. So, if KE goes down by ∆E, how does PE change? Remember Etotal is constant.