Question

speed problem
match the graph that best fits the motion from the data table.

time (sec)	distance (m)
5	15
10	30
15	30
20	30

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.