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a car with mass m traveling at speed v has kinetic energy K. What is the kinetic energy of a second car that has the same mass M and twice the speed of the first car?
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\[\color{green}{E_k = \dfrac{1}{2}mv^2}\] The kinetic energy is proportional to the square of the speed. Doubling the speed, and keeping mass constant, increases the kinetic energy by a factor of four.
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