The chart shows the movement of a ball after several seconds.
\begin{tabular}{|c|c|}
\hline A & B \\
\hline 0 & 0 \\
\hline 4 & 2.5 \\
\hline 8 & 6 \\
\hline 12 & 8 \\
\hline 16 & 10.5 \\
\hline
\end{tabular}
Column $A$ is on the $x$-axis, and Column $B$ is on the $y$ axis. Which titles should replace $A$ and $B$?
A. Column A should be "Time," and Column B should be "Position."
B. Column A should be "Position," and Column B should be "Time."
C. Column A should be "Velocity," and Column B should be "Speed."
D. Column A should be "Speed," and Column B should be "Velocity."
Answer (1)
Column A should be "Time," and Column B should be "Position." $\boxed{Column A should be "Time," and Column B should be "Position."}
Explanation
Understanding the Problem We are given a table with two columns, A and B, representing the movement of a ball. Column A is on the x-axis, and Column B is on the y-axis. We need to determine the correct titles for these columns from the given options. The data points are (0, 0), (4, 2.5), (8, 6), (12, 8), and (16, 10.5).
Analyzing Time and Position Let's analyze the data points to see if they represent a relationship between time and position. As time increases (Column A), the position (Column B) also increases. This suggests that Column A could represent time, and Column B could represent the position of the ball at that time.
Considering Alternative Arrangements Now, let's consider the other options. If Column A were 'Position' and Column B were 'Time,' it would mean that as the position increases, the time also increases, which is plausible. However, the typical way to represent motion is to show how position changes over time, not the other way around.
Ruling Out Velocity and Speed The options involving 'Velocity' and 'Speed' are less likely because we don't have enough information to directly calculate these values from the given data. We would need more information about the path of the ball to determine its velocity and speed.
Concluding the Titles Based on the analysis, the most logical choice is that Column A represents 'Time,' and Column B represents 'Position.' This aligns with the common way of representing motion and the observed trend in the data.
Examples
Understanding the relationship between time and position is fundamental in physics and everyday life. For example, when planning a road trip, you use the relationship between time and distance to estimate how long it will take to reach your destination. Similarly, in sports, athletes analyze their position over time to improve their performance. This problem demonstrates a basic application of kinematics, which is the study of motion.
