JEE Main 2023 · 10 April · morning · Single correct · +4 / −1
The position-time graphs for two students A and B returning from the school to their homes are shown in 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 (D) only
- (b) (A) and (E) only
- (c) (A), (C) and (E) only
- (d) (B) and (E) only
Answer and solution
Answer (b) (A) and (E) only
Solution
Physics sir · 4 steps
On an x–t graph, the final height of a line is how far home is, and its slope is the speed.
- Distance to home. Each line stops when the student reaches home, so the height where it ends is the distance of that home from school. A's line ends lower than B's, so A lives closer and (A) is true.
- Who is faster. The slope of an x–t line is the speed. B's line is much steeper than A's, so B travels faster and (E) is true. That makes (D) false.
- Time taken. A starts at t = 0, while B leaves school later. Both lines end at about the same time, so A spends longer on the road. (C) is false.
- So. Only (A) and (E) are correct, which is option (b).
The idea to keep. Read an x–t graph in three ways: where a line starts on the t-axis (start time), its slope (speed), and where it ends (position and arrival time).
Answer from the NTA final answer key. Solution by PrepWiser.