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Indefinite Integration problem

  1. Jul 4, 2011 #1
    1. The problem statement, all variables and given/known data
    A particle is moving with the given data. Find the position of the particle.
    [itex]a(t)=t^{2}-4t+6[/itex],
    [itex]s(0)=0[/itex],
    [itex]s(1)=20[/itex]

    2. Relevant equations

    3. The attempt at a solution
    [itex]a(t)=t^{2}-4t+6[/itex], [itex]s(0)=0[/itex], [itex]s(1)=20[/itex]
    [tex]v(t)=\int t^{2}-4t+6 dt[/tex]
    [tex]v(t)=\frac{t^{3}}{3}-2t^{2}+6t+C_{1}[/tex]
    Then I suppose I take the antiderivative again to get to s (distance), I can't solve for the constant yet.

    [tex]s(t)=\int \frac{t^{3}}{3}-2t^{2}+6t+C_{1} dt[/tex]
    [tex]s(t)=\frac{t^{4}}{12}-\frac{2t^{3}}{3}+3t^{2}+C_{1}t+C_{2}[/tex]

    So now I have two constants in there? Would I just use the parameters [itex]s(0)=0[/itex] and [itex]s(1)=20[/itex] to try to solve this like a system of 2 equations with two unknowns? I don't really know how to proceed. The other problems like this at least gave me a value for the first derivative of the original function so I could sort of work backwards.
     
    Last edited: Jul 4, 2011
  2. jcsd
  3. Jul 4, 2011 #2

    ideasrule

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    Homework Helper

    This is exactly what you do. Be more confident! :smile:
     
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