Taylor Series

  • #1

Homework Statement


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).


Homework Equations


Taylor's Series


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])
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Looks ok to me. What makes you think there is something wrong? What's your question?
 
  • #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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