To address the problem, here’s the step-by-step process you should follow:

1. Plot the Displacement vs. Time Graph:

• X-axis: Time (in seconds) ranging from 0 to 360 seconds.
• Y-axis: Displacement from the house (in meters) ranging from 0 to 245 meters.

Points to plot:

• (0, 0)
• (60, 84)
• (120, 160)
• (180, 245)
• (240, 154)
• (300, 90)
• (360, 6)

2. Calculate the Average Velocity in 3 Different Time Blocks:

Average velocity in a given time block is calculated using the formula:

$\text{Average Velocity} = \frac{\text{Change in Displacement}}{\text{Change in Time}}$

Let's calculate the average velocity for three time blocks:

Time Block 1: From 0s to 180s

• Initial displacement: 0 meters
• Final displacement: 245 meters
• Change in displacement: $245 - 0 = 245$ meters
• Change in time: $180 - 0 = 180$ seconds

$\text{Average Velocity} = \frac{245 \text{ m}}{180 \text{ s}} \approx 1.36 \text{ m/s}$

Time Block 2: From 180s to 300s

• Initial displacement: 245 meters
• Final displacement: 90 meters
• Change in displacement: $90 - 245 = -155$ meters (indicating a return towards the house)
• Change in time: $300 - 180 = 120$ seconds

$\text{Average Velocity} = \frac{-155 \text{ m}}{120 \text{ s}} \approx -1.29 \text{ m/s}$

Time Block 3: From 300s to 360s

• Initial displacement: 90 meters
• Final displacement: 6 meters
• Change in displacement: $6 - 90 = -84$ meters
• Change in time: $360 - 300 = 60$ seconds

$\text{Average Velocity} = \frac{-84 \text{ m}}{60 \text{ s}} = -1.4 \text{ m/s}$

Summary of Average Velocities:

1. 0s to 180s: 1.36 m/s (away from the house)
2. 180s to 300s: -1.29 m/s (toward the house)
3. 300s to 360s: -1.4 m/s (toward the house)

Would you like further clarification or any additional help?

Here are 5 related questions:

1. How would you describe the woman’s journey based on the displacement vs. time graph?
2. What does a negative average velocity signify in this context?
3. How would the graph look if the woman had walked at a constant velocity?
4. Can you determine the maximum speed during the trip from the data?
5. How would the displacement vs. time graph differ from a distance vs. time graph?

Tip: When plotting a displacement vs. time graph, pay close attention to the slope of the line. The slope directly represents the velocity.