Question

Question 6
The given figure 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

(a) $Speed=\frac{Distancetravelled}{Timetaken}$ = Slope of distance-time graph
Since the slope of object B is the greatest, it is travelling the fastest.
(b) The three objects are never at the same point on the road as their graphs don't coincide simultaneously at any point.


(c) On the distance axis:
7 small boxes = 4 km
Therefore,1 small box $=\frac{4}{7}km$
Initially, object C is 4 blocks away from the origin.
Therefore, initial distance of object C from origin $=\frac{4\times 4}{7}=\frac{16}{7}$
Distance of object C from origin when B passes A $=\frac{4}{7}\times 16=\frac{64}{7}$
Distance covered by $C=\frac{64}{7}-\frac{16}{7}=\frac{64-16}{7}=\frac{48}{7}=6.85km$
Hence, the total distance covered by C when B passes A is 6.85 km
(d) Distance covered by B at the time it passes C = 9 boxes
Distance traveled by B when it passes C $=\frac{4}{7}\times 9=\frac{36}{7}=5.143km$
Hence, B has traveled a distance of 5.143 km when B passes C.