If velocity triples, kinetic energy increases by what factor?

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Multiple Choice

If velocity triples, kinetic energy increases by what factor?

Explanation:
Kinetic energy grows with the square of speed. With KE = 1/2 m v^2, and mass fixed, if velocity becomes three times bigger, KE becomes 1/2 m (3v)^2 = 9 × (1/2 m v^2). So the kinetic energy is nine times larger. The other factors don’t fit because they would imply a linear or different relationship, but KE depends on v squared, so tripling speed gives a ninefold increase.

Kinetic energy grows with the square of speed. With KE = 1/2 m v^2, and mass fixed, if velocity becomes three times bigger, KE becomes 1/2 m (3v)^2 = 9 × (1/2 m v^2). So the kinetic energy is nine times larger. The other factors don’t fit because they would imply a linear or different relationship, but KE depends on v squared, so tripling speed gives a ninefold increase.

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