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. above. Choose the correct entries in the brackets below :
(a) A lives closer to the school than B
(b) A starts from the school earlier than B
(c) A walks faster than B
(d) A and B reach home at the same time
(e) A overtakes B on the road twice.

Answer 1

Hint: In a position – time graph, the vertical axis represents the position of the object or the body or of a person while the horizontal axis represents the time taken to complete the distance. To find the required solution we will use the given position-time (x-t) graphs for two children.

Complete answer:
According to the given position-time (x-t) graphs for the two children A and B returning from their school O to their homes P and Q respectively
(a) B lives closer to the school than A, because A has to cover higher distances as OP > OQ.
 (b) A starts from the school earlier than B, because ‘t = 0’ for A but for B, ‘t’ has some finite time.
(c) As the slope of B is bigger than that of A, thus B walks faster than A.
(d) A and B reach their home at different time. The value of ‘t’ corresponding to point P and Q from the x-t graph for A and B respectively is different. Since 't' is different for both, they must reach home at different time.
(e) Since, the x-t graph for A and B intersect only once. Thus, A and B meet each other only once on their way back home. As B starts from school later than A and walks faster than A, it overtakes A on his way home.
Hence, option (B) is correct.

Note:
Motion of an object or a body can be represented by a position-time graph, which plots the position of the object relative to the starting point on the y-axis and time on the x-axis. The slope of a position-time graph gives velocity of an object. The steeper the slope, faster the change in motion.