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Fig 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 $C$ ?
Solution
$(a)$ Object $B$
$(b)$ No
$(c)$ $5.714\, km$
$(d)$ $5.143\, km$
$(a)$ Speed $=\frac{\text { Distance }}{\text { Time }}$
Slope of graph $=\frac{y-\text { axis }}{x-\text { axis }}=\frac{\text { Distance }}{\text { Time }}$
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.
On the distance axis :
$7$ small boxes $= 4 \,km$
Therefore, $1 $ small box $= 4 / 7 \,Km$
Initially, object $C$ is $4$ blocks away from the origin.
Therefore, Initial distance of object $C$ from origin $= 16 / 7\, Km$
Distance of object $C$ from origin when $B$ passes $A = 8\, km$
Distance covered by $C$
