The graph shows the speed of a ball in free fall for 10 seconds. Which is the constant of proportionality shown in the graph?
Speed of a Ball in Free Fall
Plot graph titled Speed of a Ball in Free Fall. X axis labeled Time (second) with entries 0, 2, 4, 6, 8, 10 in increments of 1. Y axis labeled Speed (meters per second) with entries 0, 20, 40, 60, 80, 100 in increments of 10. Ordered pairs in diagonal line are at (1, 10); (2, 20); (3, 30); (4, 40); (5, 50); (6, 60); (7, 70); (8, 80); (9, 90): (10, 100).
CLEAR SUBMIT
110
1
10
meters per second squared
1 meter per second squared
10 meters per second squared
100 meters per second squared
The constant of proportionality shown in the graph is 10 meters per second squared.
The constant of proportionality shown in the graph is 10 meters per second squared.
To determine the constant of proportionality shown in the graph, we need to analyze the relationship between the time and the speed of the ball in free fall.
Looking at the given graph, we can observe that as time increases in a linear fashion (0, 2, 4, 6, 8, 10 seconds), the speed of the ball also increases in a linear fashion (0, 20, 40, 60, 80, 100 meters per second).
From this pattern, we can conclude that the speed of the ball is increasing at a constant rate per unit of time. In other words, we have a constant ratio between the change in speed and the change in time.
To find this constant of proportionality, we can calculate the slope of the graph. The slope represents the change in the y-axis variable (speed) divided by the change in the x-axis variable (time).
Using the ordered pairs from the graph: (1, 10); (2, 20); (3, 30); (4, 40); (5, 50); (6, 60); (7, 70); (8, 80); (9, 90); (10, 100), we can calculate the slope as follows:
Slope = (Change in y-axis variable) / (Change in x-axis variable)
Slope = (100 - 10) / (10 - 1) = 90 / 9 = 10
Therefore, the constant of proportionality shown in the graph is 10. This means that for every unit increase in time, the speed of the ball in free fall increases by 10 meters per second.
Thus, the correct answer is 10 meters per second squared.