A car is moving with a velocity of 20 m/s. The driver sees a stationary truck ahead at a distance of 100 m. After some reaction time `Deltat` the brakes are applied producing a retardation of `4 m//s^2`? What is the maximum reaction time to avoid collision ?

Explanation

After applyiing the breaks let S be the distance covered by the car before coming to rest
`v^(2)=u^(2)+2as` cover distance s
`0=20^(2)-2 xx 4s " "s=(400)/(8)=50m`
The car covers 50m after applying breaks
To avoid the clash, the remaining distance
100-50=50m must be covered by the car with uniform velocity 20m/s during the reaction time `trianglet`
`(50)/(trianglet)=20" "trianglet=(50)/(20)=2.5s`
The maximum reaction time `trianglet=2.5s`