A driver of a car travelling at 52 km hโ1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km hโ1 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?
Conversion from km/h to m/s
1 km = 1000 m
1 hour = 60 minutes = 3600 s
โด (1 ๐๐)/โ = (1000 ๐)/(3600 ๐ )
โด 1 km/h = 5/18 m/s
Car 1
Initial velocity = 52 km/h
= 52 ร 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 ร 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 โ t graph
= 1/2 ร b ร h
= 1/2 ร 5 ร 130/9
= 36.11 m
Car 2
Distance Travelled
= Area under v โ t graph
= 1/2 ร b ร h
= 1/2 ร 10 ร 5/6
= 4.166 m
So, Car 1 Travelled farther when breaks were applied
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Maninder Singh
CA Maninder Singh is a Chartered Accountant with 16+ years of practical experience and 20+ years of teaching experience. He teaches Science, Economics, Accounting and English at Teachoo using clear explanations and exam-focused methods students can trust.
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