A driver of a car travelling at the speed of `52 km h^(-1)` applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at `34 kmh ^(-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 ?

Explanation

For first driver:
initial speed `= 52 km h ^(-1)`
` = (52 xx 1000)/(60 xx 60) ms ^(-1) ~~ 14.44 ms ^(-1)`
For second driver :
initial speed `= 34 km h ^(-1)`
`= (34 xx 1000)/(60 xx 60) ms ^(-1) ~~ 9.44 ms ^(-1)`
Distance covered by the first car before coming to rest =area of `Delta AOB`
`=1/2 xx AO xx OB`
`=1/2 xx 14.44 ms ^(-1) xx 5s = 36 .1 m" "...(1)`
Distance covered by the second driver = area of `Delta COD`
`=1/2 xx CO xx OD`
`=1/2 xx 9.44 ms ^(-1) xx 10 s `
`= 47.2m " "...(2)`
From (1) and (2),
the distance travelled by the second car is more.