Train deceleration and minimum stopping distances

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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?!
 

Answers and Replies

  • #2
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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.
 
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what was the route you took?
 
  • #5
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Umm... why?
it seemed like the good option... I'm guess that wasn't the right pathway :/
 
  • #6
PeroK
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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?
 
  • #7
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While we're at it, in part one, is "##-##" the correct notation for the direction of the velocity ? given the wording of the question.
 
  • #8
jbriggs444
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it seemed like the good option... I'm guess that wasn't the right pathway :/
When in doubt, draw a picture.
1590694827873.png
 
  • #9
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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?
*CRASH*
 

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