# Taylor Series

## 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).

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:

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