20 points !
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 380 m from the crossing
and its speed is 11 m/s.
if the engineer’s reaction time is 0.43 s,
what should be the magnitude of the minimum deceleration to avoid an accident?
answer in units of m/s^2

Explanation:

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

where

u = 11 m/s is the initial velocity of the locomotive

is the reaction time

Substituting,

So the distance left between the locomotive and the car is

Now we can find the minimum deceleration to avoid the accident with the equation

where

v = 0 is the final velocity

u = 11 m/s

a is the deceleration

d = 375.3 m is the stopping distance

Solving for a,