Train Collision Stopping distance Problem

  • Thread starter SharkFin39
  • Start date
  • #1

Homework Statement



Two trains, one traveling at 74.00 km/h and the other at 148.00 km/h, are headed toward one another along a straight, level track. When they are 938 m apart, each engineer sees the other's train and applies the brakes. The brakes decelerate each train at the rate of 1.0 m/s2. Is there a collision? What distance do the trains need to allow between them to stop at this acceleration? What acceleration do the two trains need to have to stop exactly in a distance of 938 m?


Homework Equations



V^2 - Vo^2 = 2a(X-Xo) (this is what I used to solve parts 1 and 2)

The Attempt at a Solution



Well, I had no problem with the first two parts of the question. Using the above formula I determined that the first train needed 211.275m to stop, and the second needed 845.057m to stop. They needed a total distance of 1056.332m to stop, therefore there was a collision.

My question is how would I go about solving the third part of the question. The question calls for a single answer in m/s^2. Otherwise, I would've just divided the 938m by 2, and solved for two seperate accelerations. I think I'm actually more stumped by the question than the calculations. If this makes sense to anyone, I'd really appreciate some guidance. Thank you in advance for you assistance.

SharkFin
 

Answers and Replies

  • #2
mgb_phys
Science Advisor
Homework Helper
7,774
13
Use s=ut + 1/2 at^2 for each train and the 's' from both trains must add to 938m
 
  • #3
2,063
2
For the last question, consider just one train at a time. If the train 1 travelling at 74kmph was 938m away from some point (call it A), what should its deceleration be so that it comes to rest at A. Similarly for the other train.
 
  • #4
D H
Staff Emeritus
Science Advisor
Insights Author
15,393
685
For the last question, consider just one train at a time. If the train 1 travelling at 74kmph was 938m away from some point (call it A), what should its deceleration be so that it comes to rest at A. Similarly for the other train.
This won't work, for two reasons. (1) He is looking for a single number, not two numbers, and (2) the trains will crash.


The two trains have some common breaking deceleration. Call this "a". Train 1 will come to a stop after traveling some distance d1, train 2 after some distance d2. You don't know what d1 and d2 are, but you do know what they are in terms of "a" and you do know their sum.
 
  • #5
V^2 - Vo^2 = 2a(X-Xo) (this is what I used to solve parts 1 and 2)
Sharkfin. I have a very similar problem. Almost exactly but can not get your answers for x of each train's distance to stop to save my life. You converted km/h to m/s I'm pretty sure. What did u plug into each variable for that equation. a=-1.0, V=0?, Vo=74 km/h? (convert), X=?, Xo=?. Are u using X=938, Xo=unknown, V=0 (bc it stopped), Vo=20.56 m/s (after conversion), Having a hard time figuring out where the initial variables plug into the equation
 

Related Threads on Train Collision Stopping distance Problem

Replies
8
Views
224
  • Last Post
Replies
7
Views
4K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
9
Views
3K
Replies
15
Views
3K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
7K
  • Last Post
Replies
2
Views
3K
Top