A driver of a car travelling at 52 km hβ1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km hβ1 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
β΄ (1 ππ)/β = (1000 π)/(3600 π )
β΄ 1 km/h = 5/18 m/s
Car 1
Initial velocity = 52 km/h
= 52 Γ 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 Γ 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 β t graph
= 1/2 Γ b Γ h
= 1/2 Γ 5 Γ 130/9
= 36.11 m
Car 2
Distance Travelled
= Area under v β t graph
= 1/2 Γ b Γ h
= 1/2 Γ 10 Γ 5/6
= 4.166 m
So, Car 1 Travelled farther when breaks were applied

Made by

CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 12 years and a teacher from the past 16 years. He teaches Science, Accounts and English at Teachoo