What is the energy of motion called?

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Energy is the ability to do work. There are many different forms of energy: potential, kinetic, mechanical, sound, light heat, electrical, elastic, chemical, gravitational, nuclear, etc.

The energy of motion is called kinetic energy. 

The kinetic molecular theory states that all things are in motion - even the molecules of a solid. As molecules are heated, the kinetic energy increases. As the molecules gain energy, they move faster. This results in the molecules moving further and further away from one another. Thus, the particles fill more volume. Changes in kinetic energy can explain how the melting of a solid into a liquid, or the evaporation of a liquid into a gas, or the sublimation of a solid into a gas occurs. 

By definition, temperature is correlated to kinetic energy. 

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