Train deceleration and minimum stopping distances

Homework Statement:
Two trains are traveling on the same linear track but in opposite direction and toward each other. The train on the right is moving to the left with a velocity of 54 m/s and the train on the left is moving to the right with a velocity of 38 m/s. When the brakes are fully applied on the train on the right, the ensuing acceleration has a magnitude of 0.31 m/s2.

Given the trains have their breaks applied simultaneously and come to a stop at exactly the same instant,
--determine the minimum distance between the trains at which they could fully apply their brakes and come to a complete halt without colliding.
--determine the acceleration of the train on the left.
Relevant Equations:
x= 1/2at^2+Vot+Xo
a= delta v/t
So my work includes using the acceleration formula a=delta v/t

(Vrtf-Vrti)/a -> (0-54)/(-0.31) -> t=174 seconds

I plug in 174 seconds to find the acceleration of the left train. and got -0.22m/s^2

I then used the displacement equation
x=(1/2)at^2+Vo+So
coming out with Xrt=4703m and Xlt= 3281m

I subtracted those coming out with 1422m, which is the minimum distance between each train to safely halt without crashing.

is that right?!

hmmm27
Gold Member
The answer I came up with for ##distance_{initial}## (through a slightly different route that didn't include calculating the time because it isn't required) is the same as the answer you'll come up with if you doublecheck your signage.

• Delta2
what was the route you took?

haruspex
Homework Helper
Gold Member
I subtracted those
Umm... why?

Umm... why?

it seemed like the good option... I'm guess that wasn't the right pathway :/

PeroK
Homework Helper
Gold Member
2021 Award
it seemed like the good option... I'm guess that wasn't the right pathway :/
If the first train takes about ##4.7km## to stop and the second train takes about ##3.3 km## to stop, then what happens if they start about ##1.4 km## apart?

hmmm27
Gold Member
While we're at it, in part one, is "##-##" the correct notation for the direction of the velocity ? given the wording of the question.

jbriggs444 