Question

graphing situations task
part a: skills practice - answer the following questions for the road trip represented below.

1. during what interval are the travellers moving the fastest? explain your reasoning.
2. what is a possible event that occurred during the interval between d and e? explain your reasoning.
3. what type of event would cause the graph to decrease?

part b: create your own situation - create your own graph and describe the situation. title your graph and label your x and y axes. you do not need to include units. your graph and situation must include three intervals and three events.

Explanation:

Analyze the fastest interval

Using the Distance-Time Graphs and Graph Interpretation knowledge points

• Speed is represented by the slope of each segment.
• Segment \(A-B\): \(\text{slope} = \frac{20 - 0}{0.5 - 0} = 40\text{ mph}\).
• Segment \(B-C\): \(\text{slope} = 0\text{ mph}\).
• Segment \(C-D\): \(\text{slope} = \frac{110 - 20}{2 - 1} = 90\text{ mph}\).
• Segment \(D-E\): \(\text{slope} = 0\text{ mph}\).
• Segment \(E-F\): \(\text{slope} = \frac{140 - 110}{4 - 3} = 30\text{ mph}\).
• The steepest positive slope is interval \(C-D\).

Analyze the horizontal interval D to E

Using the Distance-Time Graphs and Qualitative Graphs knowledge points

• The distance remains constant at 110 miles from hour 2 to hour 3.
• A constant distance over time means speed is zero.
• This represents a stop, such as resting, eating, or refueling.

Analyze decreasing distance-time graphs

Using the Distance-Time Graphs and Qualitative Graphs knowledge points

• A decreasing line means distance from the starting point is decreasing.
• This indicates the travelers are moving back toward the start.
• An event causing this is turning around or heading home.

Answer:

Question 1

The travelers are moving the fastest during the interval C–D. This is because the line segment has the steepest slope, representing the highest speed of \(90\text{ miles per hour}\).

Question 2

A possible event during the interval D to E is a stop for lunch, a rest break, or refueling the vehicle. This is because the distance does not change, meaning the travelers are stationary.

Question 3

An event that would cause the graph to decrease is turning around and driving back toward the starting location.