An object having a mass ‘m’ moving with a velocity ‘v’ possesses a kinetic energy ‘K’. If its velocity is doubled, its kinetic energy will become:
Kinetic energy = $$\frac{1}{2}m\times v^2$$
so kinetic energy is directly proportional to $$v^2$$
because mass is constant
so new kinetic energy changes as $$(2v)^2$$ =$$4v^2$$
so kinetic energy increases 4 times
= 4k
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