Question

YO

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 0.79 s,
what should be the magnitude of the mini-
mum deceleration to avoid an accident?
Answer in units of m/s2.

Answer 1

Hi there!

We can begin by calculating the distance remaining after the reaction time.

Δd = vt

Calculate the distance traveled within this time:

Δd = (16)(.79) = 12.64 m

Subtract from the total distance:

150 - 12.64 = 137.66 m remaining

We can use the following equation to solve for the acceleration necessary:

vf² = vi² + 2ad, where vf = 0 since the train will have slowed down to rest.

Rearrange in terms of "a":

0 = vi² + 2ad

(-vi²) = 2ad

(-vi²)/2d = a

Plug in the given values:

(-(16²))/2(137.66) = a

-256/275.32 = -.9298 m/s²