# Homework Help: What is the acceleration of the train.

1. Sep 16, 2015

### astrololo

1. The problem statement, all variables and given/known data

A train is going towards a stationary car at a speed of 50 km/h. There is a distance of 250 m between the train and the car. What must be the acceleration (which is constant) of the train so that the train wont collide with the car ?

Initial position of train = 0

final position = 0,250 km - x

Speed= 50 km/h

Distance between car and train = 0,250 km

2. Relevant equations
Vfinal ^2 = v initial ^ 2 + 2*acceleration*(x final - x initial)

3. The attempt at a solution

0 = 50^2 + 2 * a * ((0,250-x)-0)

0=2500 + 2a(0,250-x)

I'm kinda stuck :/

2. Sep 16, 2015

### Bystander

What's "vfinal?"

3. Sep 16, 2015

### astrololo

4. Sep 16, 2015

### Bystander

"You" are the train. What is "vfinal?"

5. Sep 16, 2015

### astrololo

Well it's 0 km/h because I need to stop before 250 m or else I'm going to destory the car.

6. Sep 16, 2015

### Bystander

You're given velocity in km/h and distance in meters. Do you need to do any conversions?

7. Sep 16, 2015

### astrololo

Yes, I converted my 250 m to km which is 250 m * 1 km / 1000 m =0,250 km

8. Sep 16, 2015

### Bystander

Okay, European convention. What's "x?"

9. Sep 16, 2015

### astrololo

It's the position where I'll stop the train before it touches the car.

10. Sep 16, 2015

### Bystander

You've a quarter kilometer range. Does the problem statement ask for the general solution? Or, a specific value?

11. Sep 16, 2015

### astrololo

It's asking for a specific value. I could take any value of x where the train would stop before reaching the car, but I think we're really asking for a specific value where the train ALMOST reaches the car. So we're really asking for the "maximum" value of x I think.

12. Sep 16, 2015

### billy_joule

What is x here?
x final - x initial is given as 250 m in the problem statement so there's no need to have that x there.
So you have one equation with one unknown, you can solve for a. Make sure you include the correct units for your answer.

EDIT: Oh, I see they want the answer in terms of x.

13. Sep 16, 2015

### Bystander

So do I. You've picked an "awkward" unit for "a" as your work is currently set up. Might be best to consider billy joule's recommendation.

14. Sep 16, 2015

### astrololo

Ok, so I get :

0=2500 + 2ax

-2500=2ax

-1250/x=a

15. Sep 16, 2015

### billy_joule

That's not consistent with the use of x in the OP:

In words, x is the distance from the car to the where the train stops, so the maximum value of x is 250m, which corresponds to an infinite acceleration ie the train stops instantaneously. (x final position = 0.250 km - x = 0) Not likely the answer they're looking for.

For these sorts of problems it's usually safe to assume they want the answer when x = 0. That is, the train comes to a stop 'touching' the car. That corresponds to the minimum acceleration to avoid a crash.

16. Sep 16, 2015

### billy_joule

Note that x is used three times with three different meanings:

x final position = 250m - x'
xinitial position = 0

Where x' is the final train to car distance

17. Sep 16, 2015

### astrololo

So I was right in writing it this way ?

18. Sep 16, 2015

### billy_joule

Which way?

Where exactly does the problem statement end and your work begin?

Is this part of the problem statement or your own work?
If that's your own work, there was no need to introduce the additional variable x' that describes the final train-car distance. Just solve assuming the train comes to a stop at the car.
If it is part of the problem statement and they want an answer in terms of x' then your attempt in the OP is very close, just rearrange for a.

19. Sep 16, 2015

### astrololo

no, that's my attempt at the problem. The problem doesn't provide this. I did it.

20. Sep 16, 2015

### astrololo

You mean this : 0=2500+2a 0,250 ? I obtain -5000 of acceleration

21. Sep 16, 2015

### billy_joule

but what are the units?

22. Sep 16, 2015

### astrololo

0 km/h = 50 km/ h ^2 + 2 a (0,250 km - 0 km)

23. Sep 16, 2015

### billy_joule

24. Sep 16, 2015

### astrololo

wait are u telling me that my acceleration units are km/h^2 ???

25. Sep 16, 2015

### astrololo

Ok yeah, it's working now ! I got the answer ! The problem really was asking to find the acceleration at moment the train was going to percute the car. In other words, they wanted the maximum value for x and not any x before 250 m.