One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 5.0m/s, they then have the same kinetic energy.

What were the original speeds of the two cars?

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  1. M1 is the heavier car and the mass of the other car is M2 = M1/2

    (1/2) M1 V1^2 = (1/2)*(1/2)(M1/2)V2^2

    which implies that
    V1^2 = (1/4)V2^2
    V1 = V2/2

    (1/2)M1*(V1+5)^2 = (1/2)(M1/2)(V2+5)^2
    = (1/2)(M1/2)(2V1 + 5)^2
    (V1+5)^2 = (1/2)(2V1+5)^2
    V1^2 + 10 V1 + 25 = 2V1^2 + 10 V1 + 25/2
    V1^2 = 25/2
    V1 = 5/sqrt2
    V2 = 5 sqrt2

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