A tennis player moves back and forth along the baseline while waiting for her opponent to serve, producing the position-versus-time graph shown in the figure. (The vertical axis is marked in increments of 1 m and the horizontal axis is marked in increments of 4 s.)
(a) Without performing a calculation, indicate on which of the segments of graph, A, B, or C, the player has the smallest speed.
(b) Calculate the average speed for segment A.
m/s
(c) Calculate the average speed for segment B.
m/s
(d) Calculate the average speed for segment C.
m/s
a:B
b: 1
c: 2
d: .5
To determine the answers for parts a, b, c, and d, we need to analyze the position-versus-time graph that is given.
a) The speed of an object can be determined by examining the slope of the position-versus-time graph. A steeper slope indicates a higher speed, while a flatter slope indicates a lower speed.
Looking at the graph, we can determine that the segment with the smallest speed is segment C. This is because the slope of segment C is least steep compared to segments A and B.
b) To calculate the average speed for segment A, we can use the formula:
Average Speed = Total Distance / Total Time
Looking at the graph, we can see that the distance covered in segment A is 2 meters. The time interval for segment A is 4 seconds.
Plugging these values into the formula, we get:
Average Speed for segment A = 2 meters / 4 seconds = 0.5 m/s
Therefore, the average speed for segment A is 0.5 m/s.
c) Similarly, to calculate the average speed for segment B, we use the same formula:
Average Speed = Total Distance / Total Time
From the graph, we can see that the distance covered in segment B is 4 meters and the time interval is also 4 seconds.
Applying the formula, we get:
Average Speed for segment B = 4 meters / 4 seconds = 1 m/s
Therefore, the average speed for segment B is 1 m/s.
d) Lastly, to calculate the average speed for segment C, we again use the formula:
Average Speed = Total Distance / Total Time
From the graph, we can see that the distance covered in segment C is 1 meter, while the time interval is 2 seconds.
By plugging in these values, we get:
Average Speed for segment C = 1 meter / 2 seconds = 0.5 m/s
Thus, the average speed for segment C is 0.5 m/s.