Analyzing the graph:

The graph shows the distance traveled by two cars over time. The slope of each line represents the speed of the respective car.

Answers to the questions:

a. Which car is traveling faster?

Car A is traveling faster.

b. How do you know?

The slope of the line for Car A is steeper than that of Car B. A steeper slope on a distance-time graph indicates a higher speed because speed is the rate of change of distance with respect to time.

Mathematically:

• Speed = $\frac{\text{distance}}{\text{time}}$ For the same time interval, Car A covers a greater distance than Car B, proving that it is faster.

c. Can you draw a line on the graph that proves your answer for question a?

To demonstrate that Car A is faster, we can add a horizontal line at a specific distance, say 10 miles, and check the time each car takes to reach that distance:

• Car A reaches 10 miles earlier than Car B, which confirms Car A's greater speed.

Would you like me to visually enhance the graph and highlight this? Let me know!

Further Related Questions:

1. How can you calculate the exact speeds of both cars from the graph?
2. If Car B were to maintain its speed for 5 hours, how far would it travel?
3. What would the graph look like if Car B increased its speed to match Car A's?
4. How would a horizontal line on this graph relate to the cars' motion?
5. If the graph extended, how could you predict when Car B would catch up with Car A?

Tip:

When analyzing a distance-time graph, remember that the steeper the slope, the faster the speed. Always look at the rise over the run!