Question

Fig 8.11 shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions:

(a) Which of the three is travelling the fastest? 

(b) Are all three ever at the same point on the road? 

(c) How far has C travelled when B passes A? 

(d) How far has B travelled by the time it passes C?

Answer 1

∴Speed = slope of the graph

Since slope of object B is greater than objects A and C, it is travelling the fastest.

(b) All three objects A, B and C never meet at a single point. Thus, they were never at the same point on road.

(c) On the distance axis:

7 small boxes = 4 km

∴ 1 small box = 4/7 km

Initially, object C is 4 blocks away from the origin.

∴ Initial distance of object C from origin = 16/7 km

Distance of object C from origin when B passes A = 8 km

Distance covered by C = 8 - 16/7 = 65 - 16/7 = 40/7 = 5.715 km

Hence, C has travelled a distance of 5.714 km when B passes A.

(d) Distance covered by B at the time it passes C for 9 boxes = 4/7 x 9 = 36/7 = 5.143 km

Hence, B has travelled a distance of 5.143 km when B passes A.

Answer 2

(a) B is travelling fastest as he is taking less time to cover more distance. 

(b) All three are never at the same point on the road. 

(c) Approximately 6 kms.                 [as 8 – 2 = 6] 

(d) Approximately 7 kms.                 [as 7 – 0 = 7]