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Question

If the kinetic energy of a particle is tripled, by what factor has its speed increased?

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3KE=3(12mv2)3KE=3(\dfrac{1}{2}mv^{2}) 3KE=3v23KE=3v^{2} 3KE=(3v)23KE=(\sqrt{3}v)^{2}

Kinetic energy is one half mass velocity squared. If the entire kinetic energy changes, but nothing else, then we can disregard the one half and mass. We end up with 3v23v^{2}, where 3 is acting on v2v^{2}, we need a value acting on vv alone, so we take the square root of three

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