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Kinetic Energy speed and a car

  1. Apr 21, 2005 #1
    One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 8.5 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?

    first i set it up like this:
    .5 * m * v1^2 = .5 * (.5 * 2m * v2^2)

    then i get:
    v1 = v2

    then
    .5 * m * (v1 + 8.5)^2 = .5 * 2m * (v2 + 8.5)^2
    .5 * (v1 + 8.5)^2 = (v2 + 8.5)^2

    but its not right...
     
  2. jcsd
  3. Apr 21, 2005 #2

    arildno

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    Set up your conditions properly!
    1) "One car has twice the mass of a second car" [tex]m_{1}=2m_{2}[/tex]
    2) "but only half as much kinetic energy" [tex]K_{1}=\frac{K_{2}}{2}[/tex]
    3)"When both cars increase their speed by 8.5 m/s, they then have the same kinetic energy":
    [tex]\frac{m_{1}}{2}(v_{1}+8.5)^{2}=\frac{m_{2}}{2}(v_{2}+8.5)^{2}, K_{1}=\frac{m_{1}}{2}v_{1}^{2},K_{2}=\frac{m_{2}}{2}v_{2}^{2}[/tex]

    To help you along, we have:
    [tex]K_{1}=\frac{2m_{2}}{2}v_{1}^{2}=\frac{m_{2}}{4}v_{2}^{2}=\frac{K_{2}}{2}[/tex]

    Thus, we have: [tex]{v}_{1}=\frac{v_{2}}{2}[/tex]
     
    Last edited: Apr 21, 2005
  4. Apr 24, 2005 #3
    thank you, i got it now
     
  5. Feb 2, 2010 #4
    Howcome both masses are over 2?
     
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