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A car is moving with a velocity of 40 m/...

A car is moving with a velocity of `40 m//s`. the driver sees a stationary truck ahead at a distance of 200 m. After some reaction time `Delta t` the breaks are applied producing a (reaction) retardation of `8 m//s^(2)`. What is the maximum reaction time to avoid collision ?

Text Solution

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The car before coming to rest (v = 0)
`v_(2) = u^(2) + 2as to 0 = (40)^(2) - 2xx 8 xxs`
`rArr s = 100 m`
The distance travelled by the car is 100 m
To avoid the clash, remaining distance 200 -100 = 100 m must be covered by the car with uniform velocity 40 m/s during the reaction time `Delta`t.
`(100)/(Deltat) = 40 rArr Deltat = 2.5s`
The maximum reaction time `Deltat = 2.5s`
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