# Two trains headed toward each other

• goaliejoe35
In summary, the conductors of two trains on a track notice that they are headed towards each other. The velocities of the trains are given as functions of time in Figure 2-27, with a vertical scaling of 43.0 m/s. The slowing processes start when the trains are 204 m apart. The question asks for the separation between the trains when they both stop. One student attempts to solve the problem and gets d = 107.5 m for Train 1, but struggles with calculating the distance for Train 2 due to confusion about the vertical scaling on the graph. Another student suggests using the average speed formula to calculate the distance traveled by Train 2, but the first student realizes their mistake and correctly calculates the
goaliejoe35
Homework Statement

As two trains move along a track, their conductors suddenly notice that they are headed toward each other. Figure 2-27
http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c02/pict_2_27.gif

gives their velocities v as functions of time t as the conductors slow the trains. The figure's vertical scaling is set by vs = 43.0 m/s. The slowing processes begin when the trains are 204 m apart. What is their separation when both trains have stopped?

The attempt at a solution

I tried this problem and got it wrong. I was able to come up with d = 107.5 m for Train 1 but I think I am missing something when I try to calculate d for Train 2.

The part of this question that confuses me the most if when it says "The figure's vertical scaling is set by vs = 43.0 m/s." I think I don't really understand how to read the graph correctly.

Help is appreciated

Last edited:
Ok well, if 4 blocks up the side is 43m/s then what are three blocks going to represent for the velocity?

goaliejoe35 said:
I tried this problem and got it wrong. I was able to come up with d = 107.5 m for Train 1 but I think I am missing something when I try to calculate d for Train 2.
You found the distance traveled by Train 1 before it stops. Do the same thing for Train 2.
The part of this question that confuses me the most if when it says "The figure's vertical scaling is set by vs = 43.0 m/s." I think I don't really understand how to read the graph correctly.
I take that to mean that V_s = 43 m/s--which means that 4 vertical boxes = 43 m/s. So what's the initial velocity of Train 2?

Well then is this right?

if velocity equals -33 m/s then...

Train 2

Data:
v = -33 m/s
v2 = 0 m/s
t = 4s
a = ?
...then I used this equation...
v2 = v + a2t
a2 = (v2 - v) / t

= (0m/s - (-33 m/s)) / 4s

a = 8.25 m/s^2

d = (v2^2 - v^2) / 2a

= ((0m/s)2 - (-33 m/s)2) / (2(8.25m/s^2)

= -66m <--distance traveled by train 2

It doesn't equal - 33m/s exactly. There are a couple of easier ways to calculate the distance traveled. Firstly one can calculate the area under the curve to the x-axis, or you can use the average speed formula which amounts to the same thing. There's nothing wrong with the method you've used, just a bit long.

I don't quite get what you are saying by I can use the average speed formula? Isn't that formula S(avg)=(total distance traveled)/(time elapsed)? How does that relate?

goaliejoe35 said:
I don't quite get what you are saying by I can use the average speed formula? Isn't that formula S(avg)=(total distance traveled)/(time elapsed)? How does that relate?

No you're right, ignore that its a load of rubbish I was thinking of something else. Any way my main point was 33m/s is not quite the right velocity.

Ok so if 33 m/s isn't quite right how much is it off by and how else would I do this? I tried getting to the final answer using 33 m/s and my final answer was wrong so I am assuming that 33 m/s is off enough to cause me to get the problem incorrect.

What have you done to get 33m/s as the speed? Remember that 4 divisions on the y-axis is equivalent to 43m/s. What does that make 1 division equivalent to? So what velocity does 3 divisions correspond to?

Oh man...now i think i got it! 32.25 m/s ?

goaliejoe35 said:
Oh man...now i think i got it! 32.25 m/s ?

Sounds good.

goaliejoe35 said:
Ok so if 33 m/s isn't quite right how much is it off by and how else would I do this? I tried getting to the final answer using 33 m/s and my final answer was wrong so I am assuming that 33 m/s is off enough to cause me to get the problem incorrect.

If the answer is 32 m

try using areas method as mentioned before..

edit: seems like you are doing something else wrong too.. because there isn't much different between 33 and 32.5 (or maybe ...)

## 1. What is the concept of "Two trains headed toward each other"?

The concept of "Two trains headed toward each other" is a classic physics problem that involves two trains traveling towards each other on the same track at different speeds. It is often used to demonstrate the principles of relative motion and the concept of time and distance.

## 2. How do you calculate the time it takes for the trains to collide?

The formula for calculating the time it takes for the trains to collide is t = d / (v1 + v2), where t is the time, d is the distance between the two trains, and v1 and v2 are the speeds of the two trains. This formula assumes that the trains are traveling in a straight line and are not changing speeds.

## 3. What factors can affect the outcome of the "Two trains headed toward each other" problem?

The outcome of the "Two trains headed toward each other" problem can be affected by various factors, such as the initial speeds of the trains, the distance between them, and any changes in speed or direction during the course of their travel. Other factors like the weight of the trains, the condition of the tracks, and external forces like wind resistance can also have an impact.

## 4. Can this problem be applied to real-life situations?

Yes, the "Two trains headed toward each other" problem can be applied to real-life situations, such as calculating the time it takes for two vehicles traveling towards each other on the same road to collide or the time it takes for two airplanes to collide in mid-air. It can also be used to analyze the movement of particles in a chemical reaction or the motion of celestial bodies in space.

## 5. How does the "Two trains headed toward each other" problem relate to other physics concepts?

The "Two trains headed toward each other" problem relates to other physics concepts such as relative motion, speed, velocity, acceleration, and time. It also demonstrates the principle of conservation of energy and can be used to understand the relationship between distance, time, and speed in different scenarios.

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