Question

1. consider the new position - vs. time graph below for cyclists a and b.

how does the motion of the cyclist a in the new graph compare to that of a in the previous graph from page one?
b. how does the motion of cyclist b in the new graph compare to that of b in the previous graph?
c. which cyclist has the greater speed? how do you know?
d. describe what is happening at the intersection of lines a and b.
e. which cyclist traveled a greater distance during the first 5 seconds? how do you know?

Explanation:

Step1: Analyze cyclist A's motion

In the previous graph, cyclist A has a positive - slope (moving in the positive x - direction). In the new graph, cyclist A has a negative - slope (moving in the negative x - direction).

Step2: Analyze cyclist B's motion

In both graphs, cyclist B has a positive - slope, moving in the positive x - direction. The slope of cyclist B's line is the same in both graphs, so the speed and direction of cyclist B are unchanged.

Step3: Determine greater speed

Speed is given by the magnitude of the slope of the position - time graph. The slope of cyclist A's line (in magnitude) is greater than that of cyclist B's line in both graphs. So cyclist A has a greater speed.

Step4: Interpret intersection

At the intersection of lines A and B, the two cyclists are at the same position at the same time.

Step5: Compare distances in 5 seconds

For the first 5 seconds, cyclist A travels a greater distance. We can see from the graph that the change in position ($\Delta x$) for cyclist A is larger than that for cyclist B in the first 5 seconds.

Answer:

a. In the new graph, cyclist A moves in the opposite direction compared to the previous graph.
b. The motion of cyclist B is the same in terms of speed and direction in both graphs.
c. Cyclist A has a greater speed as the magnitude of the slope of its position - time graph is larger.
d. At the intersection of lines A and B, the two cyclists are at the same position at the same time.
e. Cyclist A travels a greater distance during the first 5 seconds as its change in position is larger.