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 . Choose the
.
a.` (A//B)` Iives 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//differnt) time.
e. (A//B) overtakes on the road (once//twice).

Explanation

(a)` OP lt OQ`, A lives closer to the school than (B).
(b) For ` x =0, t=0 fro A` , while (t) has some dinite value fro (B). Therefore (A) from the school earlier than (B).
(c ) Since the velocity is equal to slope of ` x-t` graph in case of uniform motion anhd slope of ` x-t` graph for (B) is greater than that for (A), hence (B) walks faster than (A).
(d) Corresponding to points ` P and ` Q`, the value of (t) from ` x-t` graphs for ` A and B` is same, which can be checked be dre=awing lines through ` P and Q` parallel to (t0 axos, Thus, ` A and b` reach home at the same time. ltbRgt (e0 The ` x=t` graph fro (A) and (B) intersect each other only once, Sinc (B) starts from the school after wanrds, therefor (B) overtakes (A) on the road once.