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

Explanation

After applying the breaks,let S be the distanc covered by the car before coming to rest.
`v^(2)=u^(2)+2as` covers distance s
`therefore0=20^(2)-2xx4s therefore= (400)/(8)=50m`
The car coveres 50 m after applying breaks
To avoid the clash,the remaining distance
100-50=50 m must be covered be 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=2.5s`