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Let's outline Jan's motion based on the description:

1. Jan starts at 5 meters from a motion sensor and walks 4 meters toward it over a period of 5 seconds.
2. She then walks 2 meters away from the motion sensor over the next 3 seconds.
3. Jan stops and waits for 2 seconds.

Here's how to draw the distance versus time graph for Jan's motion:

- Start at 5 meters at \( t = 0 \) seconds.
- At \( t = 5 \) seconds, Jan walks 4 meters towards the sensor, reaching \( 5 - 4 = 1 \) meter from the sensor.
- From \( t = 5 \) to \( t = 8 \) seconds, she walks 2 meters away from the sensor, moving to \( 1 + 2 = 3 \) meters from the sensor.
- From \( t = 8 \) to \( t = 10 \) seconds, Jan remains stationary at 3 meters from the sensor.

The graph should look like a piecewise linear plot:
- Decrease from 5 meters to 1 meter in the first 5 seconds (slope: -0.8 meters/second).
- Increase from 1 meter to 3 meters between 5 and 8 seconds (slope: +0.67 meters/second).
- Remain flat at 3 meters from 8 to 10 seconds.

Would you like to see a visual representation of this graph? Here are some further questions and tips related to the concept:

1. What does the slope of each segment on a distance-time graph represent?
2. How would the graph change if Jan walked faster or slower during each segment?
3. What is the significance of the slope changing signs on a distance-time graph?
4. How can we determine Jan's average speed during her walk?
5. What would the graph look like if Jan decided to walk in a continuous loop rather than stopping?

**Tip:** When analyzing motion on a distance-time graph, note that a steeper slope indicates faster motion, while a flat line indicates no motion.

Jan stands 5 m away from a motion sensor and then walks 4 m toward it at a constant rate for 5 s. Then she walks 2 m away from the location where she changed direction at a variable rate for the next 3 s. She stops and waits at this location for 2 s. Draw a distance versus time graph to show Jan’s motion sensor walk.

This problem focuses on Jan's motion as she walks toward and away from a motion sensor. It demonstrates how to draw a distance-time graph by analyzing constant and variable rates of motion. The solution is suitable for students in Grades 8-10 and covers key kinematics concepts like rates of change and interpreting slopes on graphs.

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