The graph in this section is designed to uncover a variety of common misunderstandings. First of all, some may interpret the graph as a picture of the trips the cars took, a flawed interpretation. If the graph has a segment that is horizontal, there may be more than one interpretation of the car's trip. The car could be stopped, or it could be going in a circle around the intersection. This is often an interesting insight for people.
Some may assume two cars that are the same distance from the intersection are side by side. Others may think that the two cars in this situation are on opposite sides of the intersection, facing each other, or that they could be approaching the intersection along intersecting streets.
A negative slope indicates that a car is moving toward the intersection. A positive slope indicates that the car is moving away from the intersection, since the distance is increasing over time. Some may wonder where the intersection is. In fact, the graph is not a picture of the car's path, but a representation of the relationship between distance and time.
Keep in mind that speed is always a positive quantity, while velocity can be positive or negative, corresponding to positive and negative slopes.
Groups: End the session by discussing Problem D5. Each group can share the "story" of their car's trip.
<< back to Part D: Speeds, Rates, Steepness, and Lines.