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If the speed of a car is halved, how does its kinetic energy change?

Work, Energy & Power

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Answer

Let speed of car be v.

Kinectic Energy at speed v = 12\dfrac{1}{2} x m x v2 = mv22\dfrac{\text{mv}^2}{2}

Kinectic Energy at speed v2\dfrac{\text{v}}{2} = 12\dfrac{1}{2} x m x (v2)2(\dfrac{\text{v}}{2})^2 = mv28\dfrac{\text{mv}^2}{8} = 14(mv22)\dfrac{1}{4}\Big(\dfrac{\text{mv}^2}{2}\Big)

Hence, when the speed of the car is halved the kinetic energy becomes one-fourth.

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