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A car is moving with a velocity of 20 m...

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.

A

5 sec

B

2.5 sec

C

4 sec

D

10 sec

Text Solution

Verified by Experts

Car covers a distance s before coming to rest using
relation as ` v^(2) = u^(2) + 2as `
` rArr s = (20xx 20)/(4xx2) = 50 ` m
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 `Delta t ` .
Hence ` (50)/(Delta t) = 20 " or " Delta t = (50)/(20) = 2.5 ` sec
Hence correct answer is (B)
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