# Taylor Series

1. Aug 11, 2008

### BoundByAxioms

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:

$$\frac{3(t-1)^{0}}{0!}$$ - $$\frac{(t-1)^{1}}{1!}$$ + $$\frac{3(t-1)^{2}}{2!}$$ - $$\frac{2(t-1)^{3}}{3!}$$. 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)+($$\frac{3}{2}$$)-($$\frac{1}{3}$$)=($$\frac{13}{6}$$)

2. Aug 11, 2008

### Dick

Looks ok to me. What makes you think there is something wrong? What's your question?

3. Aug 11, 2008

### BoundByAxioms

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!