$(a)$. Which of the three is traveling the fastest?$(b)$. Are all three ever at the same point on the road?$(c)$. How far has C traveled when B passes A?$(d)$. How far has B traveled by the time it passes C?" ">

# 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 traveling the fastest?$(b)$. Are all three ever at the same point on the road?$(c)$. How far has C traveled when B passes A?$(d)$. How far has B traveled by the time it passes C?"

Given: Distance-time graph of three objects A, B, and C in fig. 8.11.

To do: To study the given graphs and find:

$(a)$. Fastest traveling object among the three.

$(b)$. To find if all three are ever at the same point on the road.

$(c)$. To find how far has C traveled when B passes A.

$(d)$. To find how far has B traveled by the time it passes C.

Solution:

$(a)$. It is known that the slope of a distance-time graph represents the speed of the object. Here, slope B is greatest in the given distance-time graph.

So, object B is moving fastest.

$(b)$. In the given graph, lines A, B, and C never intersect at a single point. So, all the three objects are never at the same point on the road.

$(c)$. On the graph, let us mark the point of intersection of line A and line B with a blue dot. This intersecting point represents when A passes B.

From this intersecting point

On the graph, it is clearly seen that C is at 8 km when Object A passes object B.

$(d)$. On the graph below, let us mark the point where lines B and C intersect with a blue dot. this intersecting point represents where object B passes object C.

From this intersecting point, it is clearly seen that B is at 9 graph unit.

Here in the given graph, there are 7 units area of the graph from 0 to 4 km.

So, $7\ units =4\ km$

Therefore, $1\ unit=\frac{4}{7}\ km$

So, $9\ units=9\times\frac{4}{7}\ km$

$=5.14\ km$

So, object B has traveled $5.14\ km$ when it passes object C>

Updated on: 10-Oct-2022

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