__Question 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)

(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).

__Solution:__

**(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 < 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.

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