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Power as function of position

  1. Dec 8, 2009 #1
    Power to a vehicle moving along a track is alpha*x^1/2. No dissipation. alpha is constant x is distance from beginning of the track. zero initial velocity.
    What is Velocity as function of position?

    P=d KE/dt
    P=d(1/2 m v^2)/dt
    P=1/2 m d((dx/dt)^2)/dt
    P=1/2 m 2 v dv/dt
    alpha x^1/2 = 1/2 m 2 v dv/dt

    And that is as far as I get. After some random manipulations I was not able to yield anything useful. Some assistance or guidance would be greatly appreciated. Thank you.

  2. jcsd
  3. Dec 8, 2009 #2


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    Homework Helper

    dv/dt=dv/dx*dx/dt = dv/dx *v.

    use this in your last formula then solve the differential equation for v(x).

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