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Particle Motion

  1. Mar 24, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle moves in a straight line with acceleration which is inversely proportional to t3 , where t is the time. The particle has a velocity of 3ms-1 when t=1 and its velocity approaches a limiting value of 5ms-1 . Find an expression for its velocity at time t.

    2. Relevant equations
    a=-kt^3


    3. The attempt at a solution
    9qlgnb.jpg *****ROOKIE MISTAKE SHOULD BE -2/t^2 + d (last equation)***
     
    Last edited: Mar 25, 2012
  2. jcsd
  3. Mar 24, 2012 #2
    I won't answer the question directly for you, but this is just a basic algebra problem, remember that when y is proportional to x, you use the formula y=kx where k is some constant, inversly proportional to x and you have y = k/x. Once you know how y is proportional to x, and you have test values for y and x, you can plug them in and solve for k.
     
  4. Mar 25, 2012 #3
    I did some more and got stuck again, do you mind looking at it?
     
  5. Mar 25, 2012 #4
    I'm not entirely sure what you did there here's what would be a good idea:

    ∫ dv/dt dt = k∫1/t^2 dt

    v= -k/2t^2 + d

    now you know that when t=1 v=3, and you also know that the limiting velocity (when t→∞) is 5, so when t→∞, d=v, and v= 5, so d = 5, so now you have the formula

    v=-k/2t^2 + 5, and you know that when t=1, v=3.

    so just plug it in and solve for k
     
    Last edited: Mar 25, 2012
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