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Finding the Velocities

  1. Feb 24, 2006 #1
    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 7.0 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?


    let x = mass of second car
    thus mass of first car = 2.5x
    let a = speed of first car
    let b = speed of Second car

    0.5 * 2.5x * (a+7)^2 = 0.5 * x * (b+7)^2 (equation 1)

    2 * 0.5 * 2.5x * a^2 = 0.5 * x * b^2
    2.5x * a^2 = 0.5 * x * b^2 (equation)

    0.5 * 2.5x * (a+7)^2 = 0.5 * x * (b+7)^2 (equation 1)

    2 * 0.5 * 2.5x * a^2 = 0.5 * x * b^2
    2.5x * a^2 = 0.5 * x * b^2 (equation 2)

    Herre are the equations I got, but didn't get the right answers still. Help anyone?
     
  2. jcsd
  3. Feb 24, 2006 #2

    Doc Al

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    Staff: Mentor

    Your equations look OK. (They can be further simplified, of course: things can be canceled and rearranged.) Since you didn't provide your solution of the equations, I can't tell where you went wrong.
     
  4. Feb 24, 2006 #3
    I got a = 5.17 and b = 9.02 for my starting velocities.
     
  5. Feb 24, 2006 #4

    Doc Al

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    Staff: Mentor

    Describe how you solved those equations. I suggest simplifying those two equations as much as possible, then resolving them step by step.
     
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