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31 August, 19:12

One car has two and a half times the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 9.0 m/s, they then have the same kinetic energy. What were the original speeds of the two cars? first car

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  1. 31 August, 19:20
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    velocity of first car = 7.91 m

    Velocity of second car = 17.72 m/s

    Explanation:

    Let the mass of second car B is m and the kinetic energy of this car is K.

    First car A:

    mass, mA = two and half of mass of second car = 2.5 m

    Kinetic energy, KA = K/2

    Let the speed is vA.

    Second car B:

    mass, mB = m

    kinetic energy, KB = K

    Let the speed is vB.

    Kinetic energy of car B

    K = 1/2 m vB² ... (1)

    Kinetic energy of car A

    K/2 = 1/2 x 2.5 m x vA² ... (2)

    Put the value of K from equation (1), we get

    1/2 m vB² x 1/2 = 1/2 x 2.5 m x vA²

    vB² = 5 vA²

    vB = 2.24 vA ... (3)

    Now the speed of both the car is increased by 9 m/s so that thir kinetic energies are equal.

    So,

    1/2 x 2.5m x (vA + 9) ² = 1/2 x m x (vB + 9) ²

    2.5 (vA+9) ² = (vB + 9) ²

    1.58 (vA + 9) = (vB + 9)

    Put teh value of vB from equation (3)

    1.58 vA + 14.22 = 2.24 vA + 9

    vA = 7.91 m/s

    So, vB = 2.24 x vA = 2.24 x 7.9 = 17.72 m/s
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