To determine the appropriate titles for columns A and B, let's analyze the given data and the context of the question. The chart shows the movement of a ball over time. Typically, in such charts, time is plotted on the x-axis, and the dependent variable, such as position or distance, is plotted on the y-axis.
[tex]\[
\begin{array}{|c|c|}
\hline
A & B \\
\hline
0 & 0 \\
\hline
4 & 2.5 \\
\hline
8 & 6 \\
\hline
12 & 8 \\
\hline
16 & 10.5 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Solution
1. Identify the Variables:
- Column A increases consistently in whole numbers.
- Column B increases as well but not in a consistent pattern with respect to Column A.
2. Graphical Representation:
- In the context of moving objects or motion, time usually increments consistently and is plotted on the x-axis.
- The second column (B) represents some quantity that changes due to the passage of time, commonly position or displacement.
3. Pattern and Context:
- The data ([0, 4, 8, 12, 16] for A and [0, 2.5, 6, 8, 10.5] for B) suggests that column B might be recording the position of the ball at different times (seconds).
- Given that this is about movement over time, position changes due to elapsed time, making position the dependent variable and time the independent variable.
4. Verification with Physical Concepts:
- The increase in column A and the non-constant increases in column B are characteristic of real-world scenarios where time is the independent variable causing changes in another variable (position).
Based on these observations, the most appropriate titles for the columns are:
- Column A (x-axis) should be "Time."
- Column B (y-axis) should be "Position."
Therefore, the correct choice is:
Column A should be "Time," and Column B should be "Position."
