a 4000 pound car driving at 40 miles/hour has how many times the kinetic energy of another 4000 pound car driving at 10 miles/hour.

The comparison of the kinetic energy of the given bodies is required.

The first car has 16 times more the kinetic energy of the second car.

m = Mass of car = 4000 pound

[tex]v_1[/tex] = Initial velocity of car = 40 miles/hour

[tex]v_2[/tex] = Final velocity of car = 10 miles/hour

The mass of the car is constant so we have the relation

[tex]K\propto v^2[/tex]

Thus,

[tex]\dfrac{K_1}{K_2}=\dfrac{v_1^2}{v_2^2}\\\Rightarrow K_1=K_2\dfrac{40^2}{10^2}\\\Rightarrow K_1=16K_2[/tex]

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