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Homework Help: Finding position and velocity from Force (analytic mechanics)

  1. Aug 24, 2010 #1
    1. The problem statement, all variables and given/known data
    A body of mass "m" is repelled from the origin by a force F(x). The body is at rest at x_0, a distance from the origin, at t=0. Find v(x) and x(t).

    2. Relevant equations

    3. The attempt at a solution

    I first perform the following steps:


    The next step is to integrate v(x) WRT time. Doing this will solve for the position. My homework states that x(t) should be:


    If I integrate v(x) WRT time, I will get a different answer for position than the equation above. Is my expression for v(x) incorrect?
  2. jcsd
  3. Aug 25, 2010 #2
    You should integrate v(t) over time and not v(x).
    As you don't have v(t) you can instead write
    dx/dt=v(x) , separate the variables and integrate both sides.
    I mean, integrate
    dx/v(x)= dt

    You'll get t = some function of x. Then solve for x and you'll get x(t).
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