Can you make a prediction of what you think the graph would look like if a person started at 1.0m and walked slowly away for 5s, paused for 5s, then walked twice as fast toward the sensor for 5s?
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Yes, I can help you with this math problem and provide a prediction of the graph.
Let's start by breaking down the motion into different segments:
1. Walking slowly away for 5 seconds - During this time, the person is moving away from the sensor at a constant speed.
2. Pausing for 5 seconds - Here, the person is not moving, so the distance from the sensor remains constant.
3. Walking twice as fast toward the sensor for 5 seconds - In this phase, the person is moving towards the sensor at a faster speed compared to their initial movement.
To predict the graph, we need to consider the distance from the sensor over time. Let's assume the x-axis represents time in seconds, and the y-axis represents distance from the sensor in meters.
For the first segment, the person walks slowly away for 5 seconds. Let's say their speed is 0.1 m/s (for example). This means that during this phase, the distance from the sensor would decrease linearly at a constant rate of 0.1 m/s. Therefore, the graph would show a straight line with a negative slope, starting at 1.0m and gradually decreasing over time until it reaches 0.5m (since speed x time = distance, i.e., 0.1m/s x 5s = 0.5m).
During the pause phase for 5 seconds, the person is not moving, so the graph would show a flat line at 0.5m.
Finally, for the third segment, the person walks twice as fast toward the sensor for 5 seconds. Assuming a speed of 0.2 m/s (twice the speed of the previous segment), the distance from the sensor would increase linearly at a rate of 0.2 m/s. Therefore, the graph would display another straight line, starting at 0.5m and increasing over time until it reaches 1.5m (0.2m/s x 5s = 1m).
Combining these segments, the graph would look like this:
```
|
1.5 |
| ----
| ---- ----
1.0 | ---- ----
| ----
| ----
0.5 | ----
| ----
---------------------------------------
0 5 10 15 20 25 30
Time (s)
```
In the graph, the y-axis represents distance from the sensor in meters, and the x-axis represents time in seconds. The diagonal lines represent the person's movement, with negative slope indicating moving away from the sensor and positive slope indicating moving toward the sensor.
Please note that the specific numerical values (speed, distance traveled during each phase) provided in this example are arbitrary and for illustrative purposes. The actual graph would depend on the given information.
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