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 figure. Choose the correct entries in the bracket below ;
.
a.` (A//B)` lives closer to 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")`.

Explanation

(a) A lives closer to school than B.
(b) A starts from school earlier than B.
(c) B walks faster than A.
(d) A and B reach home at the same time.
(e) B overtakes A once on the road.
Explanation:(a) In the given x–t graph, it can be observed that distance OP lt OQ. Hence, the distance of school from the A’s home is less than that from B’s home.
(b) In the given graph, it can be observed that for x = 0, t = 0 for A, whereas for x = 0, t has some finite value for B. Thus, A starts his journey from school earlier than B.
(c) In the given x–t graph, it can be observed that the slope of B is greater than that of A. Since the slope of the x–t graph gives the speed, a greater slope means that the speed of B is greater than the speed A.
(d) It is clear from the given graph that both A and B reach their respective homes at the same time.
(e) B moves later than A and his/her speed is greater than that of A. From the graph, it is clear that B overtakes A only once on the road.