(adsbygoogle = window.adsbygoogle || []).push({}); 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/s^{2}), and it's jerk (rate of acceleration) was -2(m/s^{3}). 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])

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# Homework Help: Taylor Series

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