### Home > APCALC > Chapter 11 > Lesson 11.4.1 > Problem11-114

11-114.

Multiple Choice: A point traveling along the $x$-axis has position $s(t) = 2t^3 - 4t^2 + 2t + 1$. The total distance traveled by the point from $t = 0$ to $t = 2$ is:

1. $4$

1. $5$

1. $4.593$

1. $6.296$

1. $6.593$

Take the derivative and use it to determine when the point changes directions.

The point changes direction when $t = 1/3$ and $t = 1$.

$\text{total distance }=s\Big(\frac{1}{3}\Big)-s(0)-\Bigg(s(1)-s\Big(\frac{1}{3}\Big)\Bigg)+s(2)-s(1)$