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 = $5.14−0=5.14 \;km$