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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 the figure. Choose the correct entries in the brackets below;
- (A/B) lives closer to the school than (B/A)
- (A/B) starts from the school earlier than (B/A)
- (A/B) walks faster than (B/A)
- A and B reach home at the (same/different) time
- (A/B) overtakes (B/A) on the road (once/twice).
Solution
- From the graph, it's clear that OQ > OP, which indicates that A lives closer to the school than B.
- In the graph, it can be seen that for x = 0, t = 0 for A, while for x = 0, t has a specific value for B. Hence, A starts his journey from school earlier than B.
- B walks faster than A because the slope of B's graph is greater than the slope of A's graph.
- Corresponding to P and Q, the time value t from the position-time graphs for A and B is the same, that is, OE. Therefore, both A and B arrive home at the same time.
- The position-time graphs for A and B intersect at one point, specifically D, and B starts from the school later, B overtakes A on the road only once.
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