To determine the appropriate titles for Column A and Column B based on the given data and its context, we need to analyze what these columns represent.
The table provided shows a set of values for two variables denoted as Column A and Column B.
[tex]\[
\begin{tabular}{|c|c|}
\hline
$A$ & $B$ \\
\hline
0 & 0 \\
\hline
4 & 2.5 \\
\hline
8 & 6 \\
\hline
12 & 8 \\
\hline
16 & 10.5 \\
\hline
\end{tabular}
\][/tex]
Given the context of the movement of a ball over time, let's interpret these values.
Column A shows a progression from 0 to 16 in consistent intervals, while Column B shows values that increase as those in Column A increase, but not in a linear fashion. The first value (0,0) signals that when the value in Column A is zero, the value in Column B is also zero. The other values suggest that for each interval of 4 units in Column A, the corresponding value in Column B increases, although not uniformly.
Typically, in studies involving the movement of an object over time:
- The independent variable (often time, since it proceeds independently) is plotted on the x-axis.
- The dependent variable (often position, which relies on time) is plotted on the y-axis.
The progression in Column A (0, 4, 8, 12, 16) represents equal intervals, indicative of time in seconds. The corresponding values in Column B (0, 2.5, 6, 8, 10.5) likely represent the position of the ball at those respective times.
Therefore, we can conclude:
- Column A should be titled "Time" as it represents the independent variable.
- Column B should be titled "Position" as it represents the dependent variable varying with time.
Thus, the appropriate titles are:
Column A should be "Time," and Column B should be "Position."
