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A physics question

  1. Feb 7, 2005 #1
    The acceleration of a particle moving along
    the x-axis at time t is given by a(t) = 6t - 2.
    If the velocity is 25 when t = 3 and the po-
    sition is 10 when t = 1, then finnd the position
    x(t).
     
  2. jcsd
  3. Feb 7, 2005 #2

    dextercioby

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    Science Advisor
    Homework Helper

    Do you know calculus??Apply the definition of both acceleration wrt velocity & velocity wrt coordinate.
    Take care of the conditions which will fix integration constants...

    It shouldn't be 2 difficult.

    Daniel.
     
  4. Feb 7, 2005 #3

    xanthym

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    Science Advisor

    Let a(t) be the acceleration defined above, v(t) the velocity, and x(t) the x-axis position. By definition:

    [tex] v(t) = \int a(t) dt = \int (6t - 2) dt = 3t^2 - 2t + C_1 [/tex]
    [tex] x(t) = \int v(t) dt = \int (3t^2 - 2t + C_1) dt = t^3 - t^2 + C_1*t + C_2 [/tex]

    where C1 and C2 are constants. We determine the latter constants by using values given in the problem statement:

    [tex] v(3) = 25 = 3*(3)^2 -2*(3) + C_1 [/tex]
    [tex] C_1 = 4 [/tex]

    [tex] x(1) = 10 = (1)^3 - (1)^2 + (4)*(1) + C_2 [/tex]
    [tex] C_2 = 6 [/tex]

    [tex] \color{red} x(t) = t^3 - t^2 + 4t + 6 [/tex]
     
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