The position-time graphs for two students A and B returning from school to their homes are shown. Which of the following statements are correct?
A lives closer to the school
B lives closer to the school
A takes lesser time to reach home
A travels faster than B
Correct answer:A
Standard Method
Given: The position-time graphs of students A and B are straight lines starting from the school.
Find: Which statements are correct.
In a position-time graph, the slope represents speed.
From the graph, the line for A is steeper than the line for B. Therefore,
So A travels faster than B, and statement D is correct while statement E given in the source list is false. Also, for the same plotted time, the position of A is greater than that of B, so A lives farther from the school and B lives closer to the school.
Hence statement B is correct and statement A is false.
Therefore, among the four listed options here, the correct statements are B and D. The provided source answer and solution conclusion contain a discrepancy with the graph.
Graph Interpretation
A larger slope in an - graph means larger speed because
Since line A has greater slope,
so A is faster.
Also, at the same value of , the line A lies above B, which means A is at a greater distance from the school than B. Therefore B lives closer to the school.
Thus the graph supports B and D.
Assuming the steeper line means lesser speed. In a position-time graph, greater slope means greater speed. Compare the inclinations carefully.
Confusing distance from school with time taken to reach home. The vertical position shows displacement from school, while time is read on the horizontal axis.
Relying only on the printed answer key when it contradicts the graph. The graph itself must be interpreted using slope and position.
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