The table shows the kinetic energy of six balls rolling on the ground.
Ball----Velocity(m/s)---Mass(kg)---Kinetic Energy(J)
1---3---5---22.5
2---3---4---18.0
3---3---3---13.5
4---6---5---90.0
5---4---5---40.0
6---5---5---62,5
Which pair of graphs is best supported by the data in the table?
Unfortunately, as an AI text-based model, I cannot generate or display images or graphs. However, based on the data provided in the table, the best-supported pair of graphs would likely be a scatter plot or line graph that shows the relationship between Kinetic Energy (J) and Velocity (m/s) and another that shows the relationship between Kinetic Energy (J) and Mass (kg). These graphs will allow for a visual representation of the data and help identify any patterns or trends in the relationships.
To determine the pair of graphs best supported by the data in the table, we need to analyze the relationship between the velocity, mass, and kinetic energy.
First, let's plot a graph of velocity against kinetic energy.
Graph 1:
- X-axis: Velocity (m/s)
- Y-axis: Kinetic Energy (J)
Using the data from the table, we can plot the points:
Ball 1: (3, 22.5)
Ball 2: (3, 18.0)
Ball 3: (3, 13.5)
Ball 4: (6, 90.0)
Ball 5: (4, 40.0)
Ball 6: (5, 62.5)
Graph 1:
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0 1 2 3 4 5 6 7 8 9 [Velocity (m/s)]
Now let's plot a second graph of mass against kinetic energy.
Graph 2:
- X-axis: Mass (kg)
- Y-axis: Kinetic Energy (J)
Using the data from the table, we can plot the points:
Ball 1: (5, 22.5)
Ball 2: (4, 18.0)
Ball 3: (3, 13.5)
Ball 4: (5, 90.0)
Ball 5: (5, 40.0)
Ball 6: (5, 62.5)
Graph 2:
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0 1 2 3 4 5 6 7 8 9 [Mass (kg)]
Comparing the two graphs, we can see that Graph 1 (velocity vs. kinetic energy) shows a more distinct relationship between the variables. The kinetic energy increases with increasing velocity, which is consistent with the formula for kinetic energy (KE = 1/2 * mass * velocity^2). In contrast, Graph 2 (mass vs. kinetic energy) does not show a clear trend.
Therefore, the pair of graphs best supported by the data in the table is Graph 1: velocity vs. kinetic energy.