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 ?

Explanation

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.

Distance Travelled by first car before coming to rest = Area of `Delta` OPR
= (1/2)`xxORxxOP`
= `(1//2)xx5sxx52 kmh^(-1)`
= `(1//2)xx5xx(52xx1000)//3600)` m
= ` (1//2)xx5xx(130//9)` m
= ` 325//9` m
= 36.11 m
Distance Travelled by second car before coming to rest = Area of `Delta` OSQ
= ` (1//2)xxOQxxOS`
= ` (1//2) xx10sxx3 kmh^(-1)`
= `(1//2) xx10xx(3xx1000)//3600)` m
= `(1//2) xx10xx(5//6)` m
= ` 5xx(5//6)` m
= `25//6` m
= 4.16 m