(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])

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Taylor Series

**Physics Forums | Science Articles, Homework Help, Discussion**