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Constant power problem

  1. May 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Object A of mass m is pushed with a constant force, another object B of the same mass is pushed with a force that does work at constant rate. Velocity of both objects increase from v to 2v and they move a distance of s. Find the ratio of the time taken by objects A and B to move the distance s


    2. Relevant equations



    3. The attempt at a solution
    Firstly, for object A
    s = 1/2(v + 2v)t
    t = 2s/3v

    Object B has constant power, so
    change in energy = work done = 3/2 mv2
    3/2 mv2 = Pt
    v = (2Pt/3m)1/2
    integrating this term, i get
    s = 1/3 (8Pt3/9m)1/2

    But how do i eliminate m and p?
     
  2. jcsd
  3. May 8, 2010 #2

    tiny-tim

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    Hi gaobo9109! :smile:

    You really only have two unknowns, t and P/m, in your last two equations. :wink:
     
  4. May 8, 2010 #3
    but time taken for Object A to travel distance s is given by the equation t = 2s/3v. So my second equation for t should also be expressed in term of s and v so that the two equation can be divided to find the ratio. However, I have P and m in the equation instead. How can I express the second equation in term of s and v?
     
  5. May 8, 2010 #4

    tiny-tim

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    Eliminate P/m from these two equations …
     
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