Question

The position-time graphs for two students A and B returning from school to their homes are shown in the figure.

A. A lives closer to the school
B. B lives closer to the school
C. A takes lesser time to reach home
D. A travels faster than B
E. B travels faster than A
Choose the correct answer from the options given below :

• A. (A), (C) and (E) only
• B. (A) and (E) only
• C. (B) and (E) only
• D. (A), (C) and (D) only

Hint:

In position-time graphs, the slope represents speed, and the y-intercept at a given time represents distance.

Answer 1

The Correct Option is B

To solve this problem, we need to analyze the position-time graphs for students A and B as they return home from school.

1. Understanding the Graph:
   • The position-time graph indicates the distance from the school over time. The slope of the line represents the speed.
   • A steeper slope indicates a faster speed, while a gentler slope indicates a slower speed.
2. A lives closer to the school:
   • In the graph, A's line reaches the horizontal axis (time) at a smaller distance than B's. This shows A lives closer to the school.
3. B travels faster than A:
   • The line representing B has a steeper slope than A's line, indicating B travels faster.
4. Verification of Options:
   1. (A): True, as A lives closer to the school.
   2. (C): Incorrect, as A does not necessarily take less time to reach home.
   3. (D): Incorrect, as A does not travel faster than B.
   4. (E): True, as B travels faster than A.
5. Conclusion:
   • The correct answer is (A) and (E) only.