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Taylor Series

  1. Aug 11, 2008 #1
    1. The problem statement, all variables and given/known data
    Copied verbatim from the worksheet:

    At time t=1 a particle's position was 3(m), its velocity was -1(m/s), its acceleration was 3(m/s2), and it's jerk (rate of acceleration) was -2(m/s3). Use all the information given to estimate the particle's position one second later (at time t=2). Use a series method to solve this problem. (Hint: Think Taylor's series).


    2. Relevant equations
    Taylor's Series


    3. The attempt at a solution
    f(1)=3
    f'(1)=-1
    f''(1)=3
    f'''(1)=-2

    Since I'm given four derivatives at t=1, I figure I can make a Taylor series of degree 3 centered at t=1. Using the formula for Taylor series, I get:

    [tex]\frac{3(t-1)^{0}}{0!}[/tex] - [tex]\frac{(t-1)^{1}}{1!}[/tex] + [tex]\frac{3(t-1)^{2}}{2!}[/tex] - [tex]\frac{2(t-1)^{3}}{3!}[/tex]. Provided that I understand everything properly, this should be an approximation for the particle's position. So, letting t=2, I should get (3)-(2)+([tex]\frac{3}{2}[/tex])-([tex]\frac{1}{3}[/tex])=([tex]\frac{13}{6}[/tex])
     
  2. jcsd
  3. Aug 11, 2008 #2

    Dick

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    Homework Helper

    Looks ok to me. What makes you think there is something wrong? What's your question?
     
  4. Aug 11, 2008 #3
    It's for someone that I'm tutoring, and I have never done a question like that, so I'm trying to be extra careful. Thanks for your help!
     
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