### Chapter - 1 Motion

Q
##### Motion

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?

(a)

$Speed = \frac{Distance}{Time}$

Slope of graph $= \frac{y-axis}{x-axis}=\frac{Distance}{Time}$

$\therefore$ 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 = km

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

Initial distance of object C from origin $= \frac{4 \times 4}{7} = \frac{16}{7}\ km$

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

Distance covered by C $= 8 - \frac{16}{7}= \frac{56-16}{7} = \frac{40}{7}=5.714\ km$

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 = 9 boxes

Distance $=\frac{4}{7} \times 9 = \frac{36}{7} = 5.143\ km$

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

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