Ncert Exercises & Solutions

3.2 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. 3.19. Choose the correct entries in the brackets below ;

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

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

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

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

C3.19

Fig. 3.19:

(a) It is clear from the graph that OQ > OP, so A lives closer to the school than B.
(b) The position-time (x-t) graph of A starts from the origin, so x = 0, t = 0 for A while the (x-t) graph of B starts from C which shows that B starts later than A after a time interval OC. So A starts from school (O) earlier than B.

A lives closer to school than B.

c) The speed is represented by the slope or steepness of the (x-t) graph. More steeper the graph more will be the speed, so faster will be the child having a steeper graph. As the (x-t) graph of B is steeper than the (x-t) graph of A, so we conclude that B walks faster than
(d) Corresponding to P and Q, the value of t from (x-t) graphs for A and B is the same i.e. OE. So both A and B reach home at the same time.
(e) As the (x-t) graphs for A and B intersect each other at one point i.e. D and B starts from the school later, so B overtakes A on the road only once.

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