A car is moving wth a velocity of `40 m//s` the driver sees a stationary truck a head at a distance of 200 m. After some reaction time `Delta t` the breaks are applied producing a (reaction) retardation of `8 m//s^(2)`. What is the maximum reaction time to avoid collision ?

Explanation

The car before coming to rest (v=0)
`v_(2)=u^(2) +2 "as" to 0(40)^(2)-2 xx 8 xx s`
`impliess=100m`
The distance travelled by the car is `100m`
To avoid the clash, the remaining distance `200-100=100m` must be covered by the car with uniform velocity `40 m//s` during the reaction time `Deltat`.
`(100)/(Deltat)=40impliesDeltat=2.5s`
The maximum reaction time `Deltat=2.5s`