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Two undetermined constants

  1. Oct 4, 2009 #1
    1. The problem statement, all variables and given/known data

    If s(0) = 0, v(1) = 24 and a(t) = 24t+6 find s(t)

    2. Relevant equations



    3. The attempt at a solution

    I know a(t) is s''(t) and v(t) is s'(t). however, How can I find s(t)?
     
  2. jcsd
  3. Oct 4, 2009 #2

    Dick

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    Re: anti-derivative?

    Integrate a(t) twice. You get two undetermined constants. Find them by using the s(0) and v(1) conditions.
     
  4. Oct 4, 2009 #3
    Re: anti-derivative?

    We have not learnt integration yet :(. Infact, we have not even done anything from finding a function from it's derivatives.

    Is there any other way to do it?
     
  5. Oct 4, 2009 #4

    PAR

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    Re: anti-derivative?

    Have you been given any equation relating s,v, and a?
     
  6. Oct 4, 2009 #5
    Re: anti-derivative?

    Nothing at all.
     
  7. Oct 4, 2009 #6
    Re: anti-derivative?

    Find the anti-derivative of a(t), which is v(t).

    Plug in t=1 for v(t) to get the constant.

    The find the anti-derivative of v(t), which is s(t).

    Plug in t=0 for s(t) to get the constant, and now you have your answer.
     
  8. Oct 4, 2009 #7
    Re: anti-derivative?

    What is this anti-derivative? What's integration? :/
     
  9. Oct 4, 2009 #8

    PAR

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    Re: anti-derivative?

    Well either you haven't been paying attention in class or there is something seriously wrong with how they are teaching you.

    Since you haven't learned integration, the only possible way I can see you finding s(t) by derivatives only is knowing that since a(t) = 24t + 6, all of the integrals of a(t) must obey the power rule. Knowing this you know that

    v(t) = f(t^2) and s = g(t^3)

    So g(t^3) is a cubic. and can be written in the form:

    q*t^3 + b*t^2 + c*t + d

    can you solve from there?
     
  10. Oct 4, 2009 #9
    Re: anti-derivative?

    Could you not do the inverse of the power rule?
     
  11. Oct 4, 2009 #10

    PAR

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    Re: anti-derivative?

    The inverse of the power rule is integration. Since you know that

    s = q*t^3 + b*t^2 + c*t + d

    all you need to do is solve for q, b,c and d using derivatives.
     
  12. Oct 4, 2009 #11
    Re: anti-derivative?

    then s = 3qt^2 + 2bt + c?
     
  13. Oct 4, 2009 #12

    PAR

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    Re: anti-derivative?

    no, s = q*t^3 + b*t^2 + c*t + d
     
  14. Oct 4, 2009 #13
    Re: anti-derivative?

    I'm so lost right now.

    My teacher shall get angry letters >:[
     
  15. Oct 4, 2009 #14

    PAR

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    Re: anti-derivative?

    Recap: You know that s(t) is a cubic because when you take two derivatives of a cubic you get At + B which is the same form as a(t) = 24t + 6.

    So using the initial conditions eg. s(0) = 0, the a(t) formula, s(t) = q*t^3 + b*t^2 + c*t + d, and knowing that s' = v and s'' = a, solve for q,b,c, and d.
     
  16. Oct 4, 2009 #15
    Re: anti-derivative?

    Someone's been skipping class. Anti-derivative is basically doing the reverse of a derivative.

    For example the derivative of 3x^2 + 5x + 4
    = 6x + 5

    The anti-derivative of 6x + 5
    = 6x^2 * (1/2) + 5x * (1/1) + C
    = 3x^2 + 5x + C

    If the f(x) = 3x^2 + 5x + C
    and we're given f(0)=4
    then we can figure out the constant C
    and we get f(x) = 3x^2 + 5x + 4

    Hey guys, what's math? :p
     
  17. Oct 4, 2009 #16
    Re: anti-derivative?

    I think I got it! My book doesn't even have this stuff in it. No, I was not skipping class. This teacher just gives us questions we've not even seen before. He does it all the time.

    v(t) = 12t^2+6t
    s(t) = 4t^3+3t^2 + t?

    no?
    not even close?
     
  18. Oct 4, 2009 #17

    PAR

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    Re: anti-derivative?

    almost, v(t) is incorrect, redo the derivative of s(t) to find the correct v(t)
     
  19. Oct 5, 2009 #18
    Re: anti-derivative?

    am i missing the constant in the v(t)? a K right?
     
  20. Oct 5, 2009 #19

    PAR

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    Re: anti-derivative?

    Your s(t) is correct, now take its derivative to find v(t).

    yes, you are missing a constant in v(t)

    EDIT: Sorry I said that your s(t) is correct, sorry it isn't, the "t" term is wrong, you need a constant coefficient, so you need a Kt not a t. But using the initial conditions given to you, you can find what K is.
     
  21. Oct 5, 2009 #20
    Re: anti-derivative?

    You need the constant, so it's
    v(t) = 12t^2+6t+C
    to find C, you plug in the fact that you know v(1)=24

    After you find C, then you repeat the process to find s(t)
     
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