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 applying the breaks, let S be the distance covered by the car before coming to rest.
`v^2=u^2+2as` covers distance s
`therefore 0=20^2 - 2xx4s " " therefore s=400/8`=50 m
The car covers 50 m after applying breaks
To avoid the clash, the remaining distance
100 - 50 = 50 m must be covered by the car with uniform velocity 20 m/s during the reaction time `Deltat`
`therefore 50/(Deltat)=20 " " therefore Deltat=50/20=2.5 s`
`therefore` The maximum reaction time `Deltat`=2.5 s