An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. when the engineer first sees the car, the locomotive is 300 m from the crossing and its speed is 18 m/s. if the engineer’s reaction time is 0.45 s, what should be the magnitude of the minimum deceleration to avoid an accident? answer in units of m/s 2 .

- 0.56 m/s 2

Explanation:

To calculate the magnitude of deceleration to avoid the collision

distance = 300 m

initial speed = 18 m/s

reaction time ( t ) = 0.45 s

first calculate the distance traveled by the engineer/train during his reaction time

D₁ = initial speed * reaction time = 18 * 0.45 = 8.1 m

Then the remaining distance before impact between the car and Train would be

= distance - distance traveled during reaction time

= 300 m - 8.1 m = 291.9 m

from the equation of motion of objects

V² = U² + 2ax  (equation 1)

To avoid impact the final velocity( v )  would be ( 0 )

u = initial speed ( 18 m/s )

a = acceleration/deceleration ( ? )

x = remaining distance before collision ( 291.9 m )

hence equation 1 becomes

a =   =  -  = - 0.56 m/s 2

note: the answer is in negative because the Locomotive is decelerating and not accelerating

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explanation: