Question

choose the best answers using the distance - time graph. three runners are in a race. 19. choose the best answer. which table represents the movement of the runners shown by line c?

Explanation:

Step1: Calculate speed from first table

Speed \(v=\frac{\text{distance}}{\text{time}}\). For first table: \(v_1 = \frac{88}{2}=44\space m/s\), \(v_2=\frac{176}{4} = 44\space m/s\), \(v_3=\frac{264}{6}=44\space m/s\), \(v_4=\frac{352}{8}=44\space m/s\).

Step2: Calculate speed from second table

For second table: \(v_1=\frac{200}{2} = 100\space m/s\), \(v_2=\frac{400}{4}=100\space m/s\), \(v_3=\frac{600}{6}=100\space m/s\), \(v_4=\frac{800}{8}=100\space m/s\).

Step3: Calculate speed from third table

For third table: \(v_1=\frac{295}{2}=147.5\space m/s\), \(v_2=\frac{590}{4}=147.5\space m/s\), \(v_3=\frac{895}{6}\approx149.17\space m/s\), \(v_4=\frac{1180}{8}=147.5\space m/s\).

Since speed is constant in a distance - time graph (straight line), and from the graph, Line C has the lowest slope (slowest speed). The first table has the lowest speed (\(44\space m/s\)).

Answer:

First table (time (s): 2,4,6,8; distance (m):88,176,264,352)