# Train Collision Stopping distance Problem

• SharkFin39
In summary, the two trains need to have an acceleration of 1.0 m/s2 in order to stop at a distance of 938 m.
SharkFin39

## 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 separate 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

Use s=ut + 1/2 at^2 for each train and the 's' from both trains must add to 938m

For the last question, consider just one train at a time. If the train 1 traveling 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.

neutrino said:
For the last question, consider just one train at a time. If the train 1 traveling 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.

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

## 1. What is the train collision stopping distance problem?

The train collision stopping distance problem refers to the distance a train needs to come to a complete stop in the event of an emergency or unexpected obstruction on the track.

## 2. How is the stopping distance of a train calculated?

The stopping distance of a train is calculated by taking into account the train's speed, weight, and braking system, as well as external factors such as weather and track conditions.

## 3. What factors affect the stopping distance of a train?

The stopping distance of a train is primarily affected by its speed and weight. Other factors include the condition of the train's brakes, the condition of the track, and external factors such as weather conditions.

## 4. Can the stopping distance of a train be reduced?

Yes, the stopping distance of a train can be reduced by implementing various safety measures such as improved braking systems, regular maintenance of trains and tracks, and speed restrictions in certain areas.

## 5. Why is it important to consider the stopping distance of trains?

The stopping distance of trains is important to consider in order to prevent collisions and accidents. By understanding the factors that affect stopping distance and implementing safety measures, we can ensure the safety of passengers and prevent potential disasters.

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