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A driver of a car travelling at 52 km//h applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km//h 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 Text

Solution :
As given in the figure below PR and SQ are the Speed-time graph for given two cars with initial speeds 52 km `h^(-1)` and 3km`h^(-1)` respectively. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NCERT_SCI_IX_C08_E01_032_S01.png" width="80%"> <br> Distance Travelled by first car before coming to rest = Area of `Delta` OPR <br> = (1/2)`xxORxxOP` <br> = `(1//2)xx5sxx52 kmh^(-1)` <br> = `(1//2)xx5xx(52xx1000)//3600)` m <br> = ` (1//2)xx5xx(130//9)` m <br> = ` 325//9` m <br> = 36.11 m <br> Distance Travelled by second car before coming to rest = Area of `Delta` OSQ <br> = ` (1//2)xxOQxxOS` <br> = ` (1//2) xx10sxx3 kmh^(-1)` <br> = `(1//2) xx10xx(3xx1000)//3600)` m <br> = `(1//2) xx10xx(5//6)` m <br> = ` 5xx(5//6)` m <br> = `25//6` m <br> = 4.16 m

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