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Matter In Our Surroundings

Question
CBSEENSC9005656

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
left parenthesis straight i right parenthesis
Speed space of space straight A space equals space Slope space of space PN space

space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 10 minus 6 over denominator 1.1 space minus 0 end fraction

space space space space space space space space space space space space space space space space space space space space space equals 40 over 11 km divided by straight h

space space space space space space space space space space space space space space space space space space space space space equals 3.63 space km divided by straight h

Speed space of space straight B space equals space Slope space of space OM space

space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 6 minus 0 over denominator 0.7 minus 0 end fraction space

space space space space space space space space space space space space space space space space space space space space equals space 60 over 7 km divided by straight h space
space space space space space space space space space space space space space space space space space space space space equals space 8.57 space km divided by straight h

Speed space of space straight C space equals space Slope space of space QM space

space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 6 minus 2 over denominator 0.7 minus 0 end fraction space

space space space space space space space space space space space space space space space space space space space space equals 40 over 7 km divided by straight h

space space space space space space space space space space space space space space space space space space space equals space 5.71 space km divided by straight h

Thus, object B is travelling the fastest. 
(ii) No, all three objects do not meet at any point on the road. 
(iii) When B passes A at point N (at 1.2 hours), C is at a distance of 8 km from the origin O. 
(iv) B passes C at 0.7 hours. During this time B covers distance = 6 km.