The acceleration of an object is related only to objects constituting 3-dimensions (ie, those made up from protons and neutrons). Accelleration can be alternatively described as mass receiving energy via a force being applied to it. By this I mean that the energy transferred by the application of force to a 3-d object manifests itself as accelleration, and that the resulting inertia of motion (the constant motion of the object after it has been accelerated) should be measurable as an energy. Thus the energy of an object in motion should be E=mc^2 + (energy transferred by force).
This is sometimes referred to as an object taking on mass, but my reasoning here suggests that the mass of the object remains constant, with the energy transferred being manifested as motion. To explain this another way, say that an object is travelling an 10 m/s. To accelerate the object any further, a force would need to be applied that is over and above the energy required to accelerate the object from rest to 10m/s.
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