  ### Home > CALC > Chapter 4 > Lesson 4.3.1 > Problem4-100

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.

1. Find a function for $v(t)$.

Write an equation for each line segment.

2. How far north has the car traveled at $3$ hours? At $4$ hours?

Since this is a velocity graph, calculate the area under the curve for the given interval.
$\int_{0}^{3}v(t)dt$ and $\int_{0}^{4}v(t)dt=\int_{0}^{2}v(t)dt$ 1. Explain what happened to the car between $3 ≤ t ≤ 5$ hours.

For $3 ≤ t ≤ 5$, the function values are negative. This is a velocity graph, so what does negative velocity tell you about position?

2. Set up an integral to represent the displacement from $0 ≤ t ≤ 6$.

$\text{displacement }=\int_{a}^{b}\text{velocity } dt$

3. Set up an integral to represent the total distance from $0 ≤ t ≤ 6$.

$\text{total distance }=\int_{a}^{b}\text{speed } dt=\int_{a}^{b}\left | \text{velocity} \right |dt$