Question

which table represents the movement of the student shown by the red line? time (s) 0 1 2 3 distance (m) 0 1 2 3 time (s) 0 2 4 6 distance (m) 0 1 2 3 time (s) 0 1 2 3 distance (m) 0 2 4 6

Explanation:

Step1: Find the slope of the red - line

The slope $m$ of a distance - time graph gives the speed. For a straight - line distance - time graph passing through the origin $(0,0)$, the slope $m=\frac{\text{distance}}{\text{time}}$.

Step2: Analyze each table

For the first table:
When time $t = 1\ s$, distance $d = 1\ m$, slope $m_1=\frac{1}{1}=1$.
When time $t = 2\ s$, distance $d = 2\ m$, slope $m_1=\frac{2}{2}=1$.
When time $t = 3\ s$, distance $d = 3\ m$, slope $m_1=\frac{3}{3}=1$.
For the second table:
When time $t = 2\ s$, distance $d = 1\ m$, slope $m_2=\frac{1}{2}=0.5$.
When time $t = 4\ s$, distance $d = 2\ m$, slope $m_2=\frac{2}{4}=0.5$.
When time $t = 6\ s$, distance $d = 3\ m$, slope $m_2=\frac{3}{6}=0.5$.
For the third table:
When time $t = 1\ s$, distance $d = 2\ m$, slope $m_3=\frac{2}{1}=2$.
When time $t = 2\ s$, distance $d = 4\ m$, slope $m_3=\frac{4}{2}=2$.
When time $t = 3\ s$, distance $d = 6\ m$, slope $m_3=\frac{6}{3}=2$.
Since the red - line has the steepest slope among the lines in the graph, its slope is the largest. The slope of the line represented by the third table is the largest.

Answer:

The third table (time (s): 0, 1, 2, 3; distance (m): 0, 2, 4, 6)