Train deceleration and minimum stopping distances

In summary, the conversation discusses using the acceleration formula to calculate the distance between two trains to prevent a crash. The participants also discuss different approaches to solving the problem and the importance of using the correct notation for velocity.
  • #1
lol2
4
0
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?!
 
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  • #2
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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Likes Delta2
  • #3
what was the route you took?
 
  • #4
lol2 said:
I subtracted those
Umm... why?
 
  • #5
haruspex said:
Umm... why?

it seemed like the good option... I'm guess that wasn't the right pathway :/
 
  • #6
lol2 said:
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
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
lol2 said:
it seemed like the good option... I'm guess that wasn't the right pathway :/
When in doubt, draw a picture.
1590694827873.png
 
  • #9
PeroK said:
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*
 

FAQ: Train deceleration and minimum stopping distances

1. What factors affect train deceleration?

Train deceleration is affected by several factors, including the train's speed, the weight and length of the train, the condition of the track and brakes, and external factors such as weather and track grade.

2. How is train deceleration measured?

Train deceleration is measured in meters per second squared (m/s^2) or feet per second squared (ft/s^2). This is the rate at which the train's speed decreases over time.

3. What is the minimum stopping distance for a train?

The minimum stopping distance for a train depends on its speed, weight, and other factors mentioned above. On average, a train traveling at 60 mph can take up to a mile to come to a complete stop.

4. How do engineers calculate the minimum stopping distance for a train?

Engineers use a formula that takes into account the train's initial speed, deceleration rate, and other factors to calculate the minimum stopping distance. This formula is known as the Kinetic Energy formula: KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the train, and v is the initial velocity.

5. What safety measures are in place to ensure trains can decelerate and stop safely?

Trains are equipped with powerful brakes and braking systems that are regularly inspected and maintained. In addition, trains are required to follow speed limits and signals to ensure safe deceleration and stopping. Train operators are also trained to anticipate and respond to emergency situations that may require sudden deceleration and stopping.

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