Question

The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. 2.9. Choose the correct entries in the brackets below ; 

1. (A/B) lives closer to the school than (B/A) 
2. (A/B) starts from the school earlier than (B/A) 
3. (A/B) walks faster than (B/A) 
4. A and B reach home at the (same/different) time 
5. (A/B) overtakes (B/A) on the road (once/twice).
    

Answer 1

Given:

The position–time (x–t) graph shows the motion of two children A and B starting from the school O and moving towards their homes P and Q respectively.

In an x–t graph:

• Slope of the graph represents speed
• Higher final position means the home is farther from the school
• Intersection of two graphs means overtaking

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(a) (A/B) lives closer to the school than (B/A)

From the graph:

Home P (for A) is lower on the position axis than home Q (for B).

So, A’s home is closer to the school than B’s home.

Correct answer: A lives closer to the school than B.

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(b) (A/B) starts from the school earlier than (B/A)

From the graph:

The line for A starts from O at an earlier time than the line for B.

B starts later, as its graph begins to the right of A’s start.

Correct answer: A starts from the school earlier than B.

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(c) (A/B) walks faster than (B/A)

Speed is given by the slope of the x–t graph.

The line for B is steeper than that for A.

Hence, B walks faster than A.

Correct answer: B walks faster than A.

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(d) A and B reach home at the (same/different) time

From the graph:

The endpoints of both lines (at P and Q) lie on the same vertical line.

This indicates they reach their respective homes at the same time.

Correct answer: same time.

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(e) (A/B) overtakes (B/A) on the road (once/twice)

Overtaking occurs where the two graphs intersect.

From the graph, the lines intersect only once.

Since B’s graph crosses A’s graph from below, B overtakes A.

Correct answer: B overtakes A once.

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Final Answers Summary:

• (a) A lives closer to the school than B
• (b) A starts earlier than B
• (c) B walks faster than A
• (d) They reach home at the same time
• (e) B overtakes A once