Question

speed problems
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 - distance pair

For \(t = 0\ s\), \(d = 0\ m\), speed \(v_1=\frac{0 - 0}{0}=0\) (but we consider non - zero time intervals). For \(t = 0\ s\) to \(t = 5\ s\), \(d_1 = 15\ m\), \(v=\frac{15-0}{5 - 0}=3\ m/s\). For \(t = 5\ s\) to \(t = 10\ s\), \(d_2=30 - 15 = 15\ m\), \(v=\frac{30 - 15}{10 - 5}=3\ m/s\). For \(t = 10\ s\) to \(t = 15\ s\), \(d_3=30 - 30 = 0\ m\), \(v=\frac{30 - 30}{15 - 10}=0\ m/s\). For \(t = 15\ s\) to \(t = 20\ s\), \(d_4=30 - 30 = 0\ m\), \(v=\frac{30 - 30}{20 - 15}=0\ m/s\).

Step2: Analyze the motion

The object moves at a constant speed of \(3\ m/s\) from \(t = 0\ s\) to \(t = 10\ s\) and then stops (distance remains constant) from \(t = 10\ s\) to \(t = 20\ s\).

Step3: Match the graph

The graph that shows an increase in distance with a constant slope (constant speed) initially and then a horizontal line (no change in distance, zero speed) is the first graph on the top - left.

Answer:

The first graph on the top - left.