A woman walks from her house to her neighbor’s house, and back to her house. Her position has been logged by an app on her phone every 60 seconds. Here is a table of her motion data.




**Graph her walking data in a Displacement vs. Time graph** on a separate piece of graph paper.  




**Calculate the average velocity at 3 different time blocks** during the trip using the graph you made. 





Distance from House (m)

Time (s)

0

0

84

60

160

120

245

180

154

240

90

300

6

360

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.

Learn how to graph displacement vs. time and calculate average velocity using motion data of a woman walking from her house to her neighbor's house and back. Detailed step-by-step solutions and interpretations provided. Suitable for students in Grades 9-12.

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