Final answer:
Khianna's distance from home changes depending on whether she is running, jogging, or stationary. A graph of her position over time would demonstrate a changing slope as she moves, and flat segments when stationary. The slope of the line represents her velocity, and changes in the slope indicate acceleration or deceleration.
Step-by-step explanation:
In the context of Khianna's descriptions of her travels, her distance from home changes over time depending on her activities. When running home (a), her distance from home increases because she is moving away from her starting point. When jogging (b), her distance from home decreases as she is moving towards her starting point. While petting the kitten (c), there is no change in distance as she is stationary. The rate of change in these situations directly relates to her speed and mode of transportation; for instance, running may result in a steeper slope on a graph of distance versus time compared to jogging, and a flat line when she is stationary.
When asked to make a graph of position versus time, the implications are that the distance is plotted on the y-axis and the time on the x-axis. For uniform motion, such as driving at a constant velocity, the graph would be a straight line with a slope that represents velocity. However, when the rate of change varies, the slope also changes, indicating acceleration or deceleration. In Khianna's case, the graph would show segments of varying slope and horizontal segments where the distance does not change over time.
A corresponding real-world example would be delivering flyers, where one's distance increases initially, then decreases upon returning home, and then increases again as they continue the delivery route. This results in a graph with alternating segments of positive and negative slopes, and a positive slope when the person sets out once more.