Question

which of the following graphs correctly represent the data in the data table?

Explanation:

To solve this, we analyze the axes and the type of graph (linear vs. curved) based on typical distance - time relationships:

Step 1: Analyze the Axes and Relationship Type

• For a motion where distance and time have a linear relationship (constant speed), the graph of distance vs. time should be a straight line. If the relationship is non - linear, the graph is a curve.
• Let's assume the data table (not shown here, but from the context of distance - time graphs) has a linear relationship between distance and time (constant speed) or time and distance.

Step 2: Analyze Each Graph

• First Graph: Time is on the y - axis and distance on the x - axis. But usually, for motion, we plot distance on the y - axis and time on the x - axis (or vice - versa, but we check the trend). However, if we consider the slope, for a linear graph, the rate should be constant. But let's check the fourth graph.
• Second Graph: Time on y - axis, distance on x - axis, and it's a curve. This would imply a non - linear relationship (changing speed), but if the data is linear, this is incorrect.
• Third Graph: Distance on y - axis, time on x - axis, and it's a curve. Again, non - linear, so incorrect if data is linear.
• Fourth Graph: Distance on y - axis, time on x - axis, and it's a straight line. This represents a linear relationship (constant speed), which is typical for many basic motion scenarios. Also, the axes are correctly set (distance vs. time) and the linear nature matches the expected graph for constant - speed motion (which is a common case for such problems).

Answer:

The fourth graph (with Distance (meters) on y - axis, Time (seconds) on x - axis and a straight - line plot)