A driver of a car travelling at 52 km `h^(-1)` applies the brakes and accelerates uniformly in the opposite direction. The car stopped 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 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 the given two cars with initial speeds `52kmh^(-1) and 3kmh^(-1)` respectively.

Distance travelled by first car before coming to rest= Area of `DeltaOPR`
`=((1)/(2)) xx OR xx OP`
`=((1)/(2)) xx 5 xx 52kmh^(-1)`
`=((1)/(2)) xx 5 xx ((52 xx 1000))/(3600)m`
`=((1)/(2)) xx 5 xx ((130)/(9))m`
`=(325)/(9)m`
=36.11m
Distance travelled by second car before coming to rest= Area of `DeltaOSQ`
`=((1)/(2)) xx OQ xx OS`
`=((1)/(2)) xx 10 xx 3Kmh^(-1)`
`= ((1)/(2)) xx 10 xx (((3 xx 1000))/(3600)) m`
`= ((1)/(2)) xx 10 xx ((5)/(6))m`
`=(25)/(6)m`
=4.16m