Final answer:
To create position vs time and velocity vs time graphs, one must consider constant speeds and stopping periods for a student and a sprinter. The position vs time graph shows distance over time, while the velocity vs time graph indicates how velocity is constant or changes over the same period.
Step-by-step explanation:
To address the scenarios provided, we will break down the motions of both individuals and represent each as a position vs time graph and a velocity vs time graph. It is important to understand that the slope of a position vs time graph provides the velocity, and the velocity vs time graph, if constant, indicates no acceleration. If velocity changes, then the slope represents acceleration.
Confused Student Walking Through Hallways
In the first scenario, the student walks at 3 m/s for 4 seconds, then stops for 6 seconds. The position vs time graph will show a straight line with a positive slope for the first 4 seconds, followed by a horizontal line (indicating no movement) for the next 6 seconds. For the velocity vs time graph, there will be a horizontal line at 3 m/s for the first 4 seconds, then it will drop to 0 m/s for the next 6 seconds. The acceleration vs time graph will show 0 m/s² throughout since the student walks at a constant velocity and then stops.
Sprinter at a Starting Line
In the second example, a sprinter waits for 5 seconds, then sprints at 8 m/s for 5 seconds. The position vs time graph will start with a horizontal line for 5 seconds, followed by a straight line with a positive slope for the next 5 seconds as the sprinter moves at a constant velocity. The velocity vs time graph shows a line at 0 m/s for the first 5 seconds, spiking to 8 m/s for the next 5 seconds, and the acceleration vs time graph will again be 0 m/s² once the sprinter starts moving, as there is no acceleration mentioned during the sprinting interval.