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Regular Newtonian kinetic energy is 1/2 mv^2 . In this Newtonian world, the mass of something is constant, independent of velocity, in this equation. This gives a linear kinetic energy as speed goes up.
In the real Universe, this is not the case. Mass is a function of velocity, becoming infinite as velocity approaches the speed of light. This means that kinetic energy grows exponentially, as speeds approach the speed of light because while V might be increasing linearly, M is also increasing rapidly.
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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