speed problem\nmatch the graph that best fits the motion from the data table.\n| time (sec) | distance (m)…

Explanation:

Step1: Calculate speed for each time - interval

For (t = 0) to (t = 5) s, speed (v_1=\frac{\Delta d}{\Delta t}=\frac{15 - 0}{5-0}=3) m/s. For (t = 5) to (t = 10) s, speed (v_2=\frac{30 - 15}{10 - 5}=3) m/s. For (t = 10) to (t = 15) s, speed (v_3=\frac{30 - 30}{15 - 10}=0) m/s. For (t = 15) to (t = 20) s, speed (v_4=\frac{30 - 30}{20 - 15}=0) m/s.

Step2: Analyze the motion from speed values

The object moves at a constant speed for the first 10 s and then stops moving (distance remains constant) after (t = 10) s.

Step3: Match with the graph

The graph where the distance - time graph has a straight - line with a positive slope for the first part and then a horizontal line (constant distance) for the second part is the correct one.

Answer:

The graph in the top - left corner (where the distance is initially increasing linearly with time and then becomes constant) is the best match.