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 distanc 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)=50m`
The car covers 50 m 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 `Deltat`
`therefore (50)/(Deltat)=20 therefore Deltat=(50)/(20)=2.5s`
`therefore` The maximum reaction time `Deltat=2.5s`