On a foggy day two drivers spot each other when they are just 80 mts apart. They are travelling at 72 `kmh^(-1) and 60 kmh^(-1)` , respectively . Both of them applied brakes retarding their cars at the rate of `5ms^(-2) ` . Determine whether they avert collision or not .

Explanation

For the first car : u =` 72 kmh^(-1)`
`(72 xx 1000)/(3600) = 20 ms^(-1) , v = 0 , a = - 5 ms^(-2)`
As `v^(2) - u^(2) = 2as`
`:. 0^(2) - 20^(2) = 2 (-5) s, = 10 s`
Distance covered by first car , `s_(1) = 40 m,`
For the second car :
`u = 60 kmh^(-1) = (60 xx 5)/(18)`
` = (50)/(3) ms^(-1) , v = 0, a = - 5 ms^(-2)`
As `v^(2) - u^(2) = 2as`
`:. 0^(2) - ((50)/(3))^(2) = 2 (-5) s`
Distance covered by second car,
`s_(2) = (2500)/(9 xx 10) = 27 . 78`
Total distance covered by the two cars
`rArr s_(1) +s_(2) = 40 + 27 . 78 = 67 . 78 m `
As this distance is less than the initial distance (-80m) between the two cars,so the collision will be averted .