### Home > CALC > Chapter 11 > Lesson 11.4.1 > Problem11-129

11-129.
1. Multiple Choice: A point traveling along the x-axis has position
s(t) = 2t3 − 4t2 + 2t + 1.
The total distance traveled by the point from t = 0 to t = 2 is: Homework Help ✎

1. 4

2. 5

3. 4.593

4. 6.296

5. 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.

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