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Distance moved as a function of time

  1. May 22, 2006 #1
    Sir,
    A body is moved along a straight line by a machine delivering constant power. It is said that the distance moved by the particle in time t is proportional to t^(3/2). Can you please explain how this is derived?
    Here the symbol ^ represents power.
     
  2. jcsd
  3. May 22, 2006 #2

    Meir Achuz

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    P=Fv=v m dv/dt=(m/2)d/dt(v^2), so
    v^2=(2P/m)t.
    Then, dx/dt=(2P/m)^1/2 t^1/2,
    and x=(2/3)(2P/m)t^3/2.
    This assumes x=-0 and v=0 agt t=0.
     
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