5. 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?
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Answer:
Explanation:
As given in the figure below PR and SQ is the Speed-time graph for given two cars with initial speeds 52 km/hr and 3 km/hr respectively.
Distance Travelled by first car before coming to rest =Area of Δ OPR
= (1/2) × OR × OP
= (1/2) × 5 s × 52 kmh-1
= (1/2) × 5 × (52 × 1000)/3600) m
= (1/2) × 5 × (130/9) m = 325/9 m
= 36.11 m
Distance Travelled by second car before coming to rest =Area of Δ OSQ
= (1/2) × OQ × OS
= (1/2) × 10 s × 3 kmh-1
= (1/2) × 10 × (3 × 1000)/3600 m
= (1/2) × 10 × (5/6) m
= 5 × (5/6) m
= 25/6 m
= 4.16 m
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