A tennis player moves back and forth along the baseline while waiting for her opponent
to serve, producing the position vs time graph shown below:
a. Without performing a calculation, indicate on which segments of the graph, A, B or C,
the player has the greatest speed.
b. Calculate his speed for segments A, B and C.
See similar questions below.
To determine the segments where the tennis player has the greatest speed, we need to look at the slope of the position vs. time graph. The steeper the slope, the greater the speed of the player.
A. To find the segment with the greatest speed without performing the calculation, we look for the steepest slope on the graph. Steeper slopes correspond to faster movement.
B. To calculate the speed for segments A, B, and C, we need to calculate the slope of each segment. The slope represents the rate of change of position with respect to time, which is equal to the speed.
To calculate the speed for each segment, we can choose two points on each segment and use the formula:
Speed = (Change in position) / (Change in time)
Let's label the points on the graph for each segment:
Segment A: Point A1 (t1, x1) and Point A2 (t2, x2)
Segment B: Point B1 (t3, x3) and Point B2 (t4, x4)
Segment C: Point C1 (t5, x5) and Point C2 (t6, x6)
Now, let's perform the calculation to find the speed for each segment:
Segment A:
Speed_A = (x2 - x1) / (t2 - t1)
Segment B:
Speed_B = (x4 - x3) / (t4 - t3)
Segment C:
Speed_C = (x6 - x5) / (t6 - t5)
By calculating the above expressions, we can find the speeds for each segment and compare them to determine the greatest speed.