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Motion under a direct-square force.

  1. Oct 16, 2004 #1


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    I've heard it said that two particles repelling each other by a force that increases in direct proportion to their separation will raise that separation to infinity in finite time...under classical, non-relativistic physics, of course.

    Does anyone happen to have the derivation? :confused:

    Jerry Abbott
  2. jcsd
  3. Oct 16, 2004 #2


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    Just integrate the equation of motion which can be written in generic form as

    [tex]\frac {d^2x}{dt^2} = x^2[/tex]

    to find

    [tex]\frac {dx}{dt} = \sqrt {v_0^2 + \frac {2}{3} \left( x^3 - x_0^3 \right)[/tex]

    from which it follows that the particles can make it to infinity in finite time.
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