A driver of a car travelling at 52 km h–1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km h–1 in another car applies his brakes slowly and stops in 10 s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?
Answer
First, let us convert both speeds in m/s
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Conversion from km/h to m/s
1 km = 1000 m
1 hour = 60 minutes = 3600 s
∴ (1 𝑘𝑚)/ℎ = (1000 𝑚)/(3600 𝑠)
∴ 1 km/h = 5/18 m/s
Car 1
Initial velocity = 52 km/h
= 52 × 5/18 m/s
= 130/18 m/s
= 14.44 m/s
Final Velocity = 0 m/s
Time = 5 second
Car 2
Initial velocity = 3 km/h
= 3 × 5/18 m/s
= 5/6 m/s
= 0.833 m/s
Final Velocity = 0 m/s
Time = 10 second
Car 1
Distance Travelled
= Area under v − t graph
= 1/2 × b × h
= 1/2 × 5 × 130/9
= 36.11 m
Car 2
Distance Travelled
= Area under v − t graph
= 1/2 × b × h
= 1/2 × 10 × 5/6
= 4.166 m
So, Car 1 Travelled farther when breaks were applied
CA Maninder Singh is a Chartered Accountant for the past 13 years and a teacher from the past 17 years. He teaches Science, Economics, Accounting and English at Teachoo
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