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?

Question

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?

shane_b · Answer

Ok, let's start by writing everything out:

d=150m
v=16m/s
reaction time = 0.75s

First figure out how much closer the train got in the 0.75s before the engineer started braking:
$$(0.75s)(16m/s)=12m$$Therefore, he needs to stop in $$150m-12m=138m$$
Now just use the kinematic equation:$$V_f^2=V_i^2+2ad$$Plug in values:$$(0m/s)^2=(16m/s)^2+2a(138m)$$Solving for a you should end up with a braking acceleration of 0.93m/s^2.  This could be negative depending on your coordinate system.

anonymous · Answer

Thank you so much!
I got it down to the basics but I didn't know which equation to use,

shane_b · Answer

No problem, good luck :)