CPM Homework Help : CALC Problem 4-100

The graph at right shows the velocity (in miles per hour) of a car during a road trip. At time $t = 0$ , the car was on the Golden Gate Bridge heading north.

Find a function for $v(t)$ .
Hint (a):
Write an equation for each line segment.
How far north has the car traveled at $3$ hours? At $4$ hours?
Hint (b):
Since this is a velocity graph, calculate the area under the curve for the given interval.
$\int_{0}^{3}v(t)dt$ and $\int_{0}^{4}v(t)dt=\int_{0}^{2}v(t)dt$

Explain what happened to the car between $3 ≤ t ≤ 5$ hours.
Hint (c):
For $3 ≤ t ≤ 5$ , the function values are negative. This is a velocity graph, so what does negative velocity tell you about position?
Set up an integral to represent the displacement from $0 ≤ t ≤ 6$ .
hint (d):
$\text{displacement }=\int_{a}^{b}\text{velocity } dt$
Set up an integral to represent the total distance from $0 ≤ t ≤ 6$ .
hint (e):
$\text{total distance }=\int_{a}^{b}\text{speed } dt=\int_{a}^{b}\left | \text{velocity} \right |dt$