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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 160 m from the crossing and its speed is 29 m/s.
If the engineer’s reaction time is 0.22 s, what should be the magnitude
of the minimum deceleration to avoid an accident?
Answer in units of m/s^2
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In 0.22 of a second, the locomotive moves forward 29*0.22 = 6.38 meters.
The remaining distance to the car is 160 - 6.38 = 153.62 meters.
At the time moment t= 0.22 s, the locomotive starts decelerating.
We assume that the deceleration value remains constant.
At this condition, the average rate to the stop is 29/2 = 14.5 m/s.
Thus the time decelerating to the full stop is = 10.59448276 seconds.
The uniform deceleration value is = 2.737273792.
ANSWER. The minimum uniform deceleration is about 2.74 m/s^2.
Solved.