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 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 :
Show Hint
In position-time graphs, the slope represents speed, and the y-intercept at a given time represents distance.
(A), (C) and (E) only
(A) and (E) only
(B) and (E) only
(A), (C) and (D) only
The Correct Option is B
Solution and Explanation
Step 1: Identify the Slopes
The slope of A is given as:
\( \text{slope}_A = V_A \)
The slope of B is given as:
\( \text{slope}_B = V_B \)
Step 2: Compare the Slopes
Since:
\( \text{slope}_B > \text{slope}_A \)
It follows that:
\( V_B > V_A \)
Step 3: Relate Velocity to Time
As velocity (\( V \)) is inversely related to time (\( t \)) for a given distance:
\( t_B < t_A \)
Conclusion:
The final answer is: (A) and (E) only.
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