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

Options

A. 5 sec
B. `2.5 sec`
C. 3 sec
D. `3.5 sec`

Answer

B

Explanation

Car covers a distance is before coming to rest using relation as `v^(2) = u^(2) + 2as`
`rArr s = (20 xx 20)/(4 xx 2) = 50 m`
To avoid the clash the remaining distance `100 - 50 = 50m` must be covered by the car with uniform velocity `20 m//s` during the reaction time `Deltat`.
Hence `(5)/(Delta t) = 20` or `Delta t = (50)/(20) = 2.5 sec`