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Kinetic energy is the energy associated with an object’s motion through space. We used to think that when an object of mass m was moving at speed v, its kinetic energy was KE = 1/2 m v^(2). This seemed to match experiment – if we put some amount of energy into an object, this formula accurately predicted how fast it would go.
However in the early 1900s Einstein and others discovered that our laws of movement theoretically failed at high speeds, because they would be inconsistent with the laws of electromagnetism. The correct laws actually predicted that when an object reached some speed v, it would have more than 1/2 m v^(2) kinetic energy, and if the speed was close to the speed of light it would be a lot more. At low speeds this difference is too small to measure, but in particle accelerators we can in fact measure this energy gap, and measure that the prediction given by special relativity is accurate (though it’s a little bit too long to write out here).
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