Brain dropping: Kinetic energy is a type of potential energy

In Chemistry class today we talked about forms of energy. I've always been a little irked by the notion that there are two main forms of energy, kinetic and potential, but it's never been annoying enough to grab my focus. Today, however, I formed a definition of kinetic energy that puts it squarely within the realm of potential energy.

Wikipedia defines potential energy as "energy stored within a physical system" and kinetic energy as "energy [an object] possesses due to its motion". That's good enough for applied science, I suppose.

When an object is accelerated to a new velocity, it enters a new inertial frame of reference distinct from the observer or the initial frame. Much as potential energy is gained by placing an object on a high shelf, kinetic energy is gained by placing an object in a different inertial frame. The former derives from movement against gravity, and the latter derives from movement against inertia. In other words, both are components of the state of the physical system.

So can we agree that kinetic energy is just a type of potential energy?

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