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 200 m from the crossing
and its speed is 13 m/s.
if the engineer’s reaction time is 0.46 s,
what should be the magnitude of the minimum deceleration to avoid an accident?
answer in units of m/s²

Explanation:

First of all, we need to calculate the distance covered by the locomotive during the reaction time, which is

t = 0.46 s

During this time, the locomotive travels at

v = 13 m/s

And the motion is uniform, so the distance covered is

The locomotive was initially 200 m from the crossing, so the distance left to stop is now

And now the locomotive has to slow down to a final velocity of in this distance. We can find the minimum deceleration needed by using the suvat equation:

where

v = 0 is the final velocity

u = 13 m/s is the initial velocity

a is the deceleration

d = 194.0 m is the distance to stop

Solving for a,