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

Answer 1

The two children are A and B and the homes are P and Q respectively and the school is O.

The given graph is shown below.

a)

The distance OP is less as compared to distance OQ so the distance of the school from the home of A is less than that from the home of B.

Thus, the child A lives closer to school than child B.

b)

If child A is at origin then child B will be at some finite value on t−axis.

Thus, child A starts from school earlier than the child B.

c)

The slope of the distance-time graph gives the speed so it can be observed that the slope of child B is greater than the slope of child A.

Thus, child B walks faster than A.

d)

According to the above graph, the timings of both child A and B to reach home is same.

Thus, child A and B reach home at the same time.

e)

The speed of child B is greater than the speed of child A and child B moves later than child A.

Thus, child B overtakes the child A only once on the road.