Question

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

1. Which of the three is travelling the fastest? 
2. Are all three ever at the same point on the road? 
3. How far has C travelled when B passes A? 
4. How far has B travelled by the time it passes C?

Answer 1

(a) Object B
\(Speed = \frac{Distance }{ Time}\) 
= \(Slope \;of \;graph = \frac{y - axis }{ x - axis}\) 
= \(\frac{Distance }{ Time}\)
Therefore, Speed = slope of the graph 
Since slope of object B is greater than objects A and C, it is travelling the fastest. 

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(b) No 
All three objects A, B and C never meet at a single point. 
Thus, they were never at the same point on road. 

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(c) 5.714 km 
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 = \(\frac{16 }{ 7}\) \(Km\) 
Distance of object C from origin when B passes A = \(8\) \(km\) Distance covered by C.

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(d) 5.143 km
Position of B at the instant it passes C is, \(4+2×0.57=5.14 \;km\)
∴ Distance traveled by B = \(5.14−0=5.14 \;km\)