Question

interpreting d-t graphsscenario 1: the three little pigsthe graph below represents the story of \the three little pigs.\ the parts of the story are listed below the graph. follow along the story and notice how the wolfs position changes on the graph. label the parts of the graph with the appropriate number, and then answer the questions that follow.position-time graph of the wolf in the three little pigs1. the wolf started from his house (the origin).2. he traveled to the straw house (the line moves upward).3. stayed to eat dinner and blow the house down (the line is flat because position is not changing).4. traveled to the stick house (the line moves upward again).5. again stayed, ate seconds, and blew the house down (the line is flat).6. traveled to the brick house (the line moves upward).7. died in the stew pot at the brick house (the line is flat).questions - show all work and units!1. which house was the wolf at the longest? ____the shortest? ____2. to which house did the wolf travel the fastest? how do you know?3. what was the wolfs instantaneous speed at 30 seconds? 60 seconds? 85 seconds?

Explanation:

Step1: Calculate time at straw house

Time at straw house: $20 - 5 = 15$ seconds

Step2: Calculate time at stick house

Time at stick house: $80 - 40 = 40$ seconds

Step3: Calculate time at brick house

Time at brick house: $120 - 90 = 30$ seconds

Step4: Compare times for Q1

Compare 15, 40, 30: longest = stick house, shortest = straw house

Step5: Calculate speed to straw house

Speed to straw house: $\frac{5-0}{5-0} = 1$ m/s

Step6: Calculate speed to stick house

Speed to stick house: $\frac{14-5}{40-20} = \frac{9}{20} = 0.45$ m/s

Step7: Calculate speed to brick house

Speed to brick house: $\frac{32-14}{90-80} = \frac{18}{10} = 1.8$ m/s

Step8: Compare speeds for Q2

Compare 1, 0.45, 1.8: fastest to brick house (steepest line)

Step9: Find speed at 30s (flat line)

Flat line = no movement, speed = $0$ m/s

Step10: Find speed at 60s (flat line)

Flat line = no movement, speed = $0$ m/s

Step11: Find speed at 85s (rising line)

Rising line = constant speed = $1.8$ m/s

Answer:

1. Longest: The stick house; Shortest: The straw house
2. The wolf traveled fastest to the brick house. This is because the line segment for this trip is the steepest on the position-time graph, and steeper lines represent higher speed.
3. 30 seconds: $0$ m/s; 60 seconds: $0$ m/s; 85 seconds: $1.8$ m/s