Question

Two students were asked to plot a distance-time graph for the motion described by Table A and Table B. The graph given in Figure is true for

Table A \begin{tabular}{|c|c|c|c|c|c|c|} \hline Distance moved \( ( m ) \) & 0 & 10 & 20 & 30 & 40 & 50 \\ \hline Time (minutes) & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline \end{tabular} Table B \begin{tabular}{|c|c|c|c|c|c|c|} \hline Distance moved (m) & 0 & 5 & 10 & 15 & 20 & 25 \\ \hline Time (minutes) & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \end{tabular}
Fig 13.2

• A. Both A and B
• B. A only
• C. B only
• D. Neither A nor B

Answer 1

The correct option is A

Both A and B

Step 1: The distance-time graph

The distance covered by an object at any instance can be determined by using a distance-time graph.

1. In the distance-time graph, the distance is indicated along the Y-axis, and the time is indicated along the X-axis.
2. If the motion of the object is uniform, the graph will be a straight line.
3. The slope of the straight-line graph is the same irrespective of the interval which is chosen.
4. That means the speed of an object under uniform motion remains constant and it is $5\mathrm{m}/\min$.

Step 2: Consider table A

The plotted graph by the student using table A can be shown as follows:

The slope for each instance can be calculated as follows:

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{10-0}{2-0} \\ m=5 \end{gathered}$$

Where, $m$ is the slope.

The slope of the distance-time graph is the same as the slope given in the diagram.

For any two points, the slope remains the same.

Hence, the given graph is true for table A.

Step 3: Consider the table B

The plotted graph by the student using table B can be shown as follows:

The slope for each instance can be calculated as follows:

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5-0}{1-0} \\ m=5 \end{gathered}$$

The slope of the distance-time graph is the same as the slope given in the diagram.

For any two points, the slope remains the same.

Hence, the given graph is true for table B.

Therefore, the graph is true for both tables A and B.

Hence, option (A) is correct.