Question

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Explanation:

Analyze the fastest interval

Using the Distance-Time Graphs and Graph Interpretation knowledge points

• The speed is represented by the slope of each line segment.
• Segment \(C-D\) goes from \(t = 1\) to \(t = 3\) hours, rising from \(20\) miles to \(100\) miles.
• Slope of \(C-D\) is \(\frac{100 - 20}{3 - 1} = 40\text{ mph}\).
• Segment \(A-B\) rises \(20\) miles in \(0.5\) hours (slope = \(40\text{ mph}\)).
• Segment \(E-F\) rises \(40\) miles in \(1.5\) hours (slope \(\approx 26.7\text{ mph}\)).
• The steepest segments are \(A-B\) and \(C-D\).

Interpret the horizontal interval D-E

Using the Distance-Time Graphs and Qualitative Graphs knowledge points

• Between \(D\) and \(E\), the time increases from \(3\) to \(3.5\) hours, but the distance remains constant at \(100\) miles.
• A flat, horizontal line on a distance-time graph indicates that the position is not changing.
• This represents a stop where the travelers are stationary (e.g., stopping for lunch, gas, or a break).

Determine what causes a decrease

Using the Distance-Time Graphs and Qualitative Graphs knowledge points

• The vertical axis represents distance from the starting point.
• A decreasing line means the distance from the starting point is getting smaller.
• This represents the travelers turning around and driving back toward their starting location.

Answer:

Question 1

The travelers are moving the fastest during intervals A-B and C-D.

Reasoning: The speed is represented by the steepness (slope) of the line. Both intervals \(A-B\) and \(C-D\) have the steepest upward slope of \(40\text{ miles per hour}\).

Question 2

A possible event is stopping for a break, gas, or lunch.

Reasoning: The horizontal line between \(D\) and \(E\) shows that time is passing but the distance traveled does not change, meaning the vehicle is completely stopped.

Question 3

An event that would cause the graph to decrease is driving back toward the starting point.

Reasoning: A downward slope means the distance from the starting location is decreasing, which indicates returning or traveling in the opposite direction.