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 150 m from the crossing
and its speed is 16 m/s.
If the engineer’s reaction time is 0.75 s,
what should be the magnitude of the mini�mum deceleration to avoid an accident?
Answer in units of m/s
before the brakes: 0.75 s * 16 m/s = 12 meters at full speed
We now have 150 - 12 = 138 meters to stop
average speed during stop = 16/2 = 8 m/s
so
time to stop = 138 m / 8 m/s = 17.25 s
change in speed = -16 m/s
time = 17.25 s
so
a = - 16 m/s / 17.25 s = - 0.928 m/s^2
again note acceleration in m/s^2 not m/s