# Motion Problems

1. Dec 23, 2009

### fireemblem13

These are bonus problems for a Physics 1710 class.

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

A train is decelerating with initial velocity 10 m/s. What should be the acceleration of the train for stopping in 3 seconds at distance of 8m.

2. Relevant equations

3. The attempt at a solution

L=vt + at^2 /2
a=2(L-vt)/t^2
Substituting in, gives a=-4.89
Apparently, this is wrong.

Another problem.

Two friends are traveling by train, and they have nothing to do. They decide
to measure the speed of train. The first one starts counting rails of the railroad. He knows
that the length of one rail is 10 meters, and it takes him 3 minutes to count 156 rails. He
calculated that the speed is equal to 31.2 km/hour. The second one starts counting pillars
along the railroad. He has counted 32 pillars, and this takes him 3 minutes (he knows that
the distance between pillars is 50 meters). He calculates that the speed is 32 km/hour. Who
makes a mistake, and what is the speed of the train?

I said the second person was wrong, since he was counting the distances between pillars, so the first person must be right and the velocity must be 31.2 km/h. Apparently this is wrong too.

Any help appreciated.

2. Dec 23, 2009

### cepheid

Staff Emeritus
Hi fireemblem13, welcome to PF!

Was this graded by a computer that told you you were wrong, or a person? You are on the the right track, but you need to be more specific about what the pillar-counting person did wrong. There is nothing inherently wrong with his method, he just calculated the wrong thing. What he is doing is different from what the rail-counting person is doing. The rail-counting person is counting the actual number of length intervals covered, and hence the total distance. The pillar-counting person is counting the number of end-points or boundaries between those length intervals.

To put it another way: is the number of pillars equal to the number of pillar spacings?

Last edited: Dec 23, 2009
3. Dec 23, 2009

### fireemblem13

This was my professor of mine who graded it. To answer your question, no the number of pillars is not equal to the number of pillar spacings. The number of pillar spacings is one less, 31. Therefore, he should've calculated the velocity as 31km/h. I did this in my solution, and said the velocity therefore must be 31.2 since the first person counts the entire distance the train covers, but... nope.

4. Dec 23, 2009

### diazona

fireemblem13, for your first problem, your answer doesn't have any units. To put it another way, you were supposed to get an acceleration, but you got a number. That means it can't be right. Try including the proper units...

For the second problem, the issue that cepheid pointed out would apply just as well to the person counting rails as well.

5. Dec 23, 2009

### cepheid

Staff Emeritus
Ohhhh I see. This problem is not worded well at all. Because it said that, "the length of a rail is 10 m," I assumed that "rails" were discrete sections out of which the track was made (i.e. that they ran parallel to the track). But, if you assume that "rails" are actually the crosswise pieces that run between the two edges of the track, and that the spacing between them is 10 m (NOT their length), then it means that both people made the same mistake, and both should have measured a distance of 155 m in 3 minutes. You should ask your prof if that's what he meant (and also complain that he didn't define very well what a "rail" was).

EDIT: diazona posted while I was typing.

6. Dec 23, 2009

### fireemblem13

Im pretty sure i didnt miss the first problem because of units. I was just on the phone with him, and he said plug in the acceleration and see what final velocity you get. Plugging in a=-4.89 the final velocity isnt 0. That made me think, why not just use a=(vf-vi)/t to get a=-10/3. Of course with this a, the train stops in 15m. But maybe the length of the train is 7m or something? I dont really know.

@cepheid I suppose that could be the problem. Both of them messed up and the velocity is 31.

7. Dec 23, 2009

### diazona

I agree, this is a poorly worded problem. Besides the confusion over what a "rail" is, the problem also isn't specific about how each person made their count. They could have picked a post or rail to mark a starting point and then counted the number of posts/rails after that, which would be perfectly legitimate, and then it'd just be a rounding issue. Only the fact that subtracting 1 from the count yields the same answer in both cases suggests that that was probably the answer.

8. Dec 23, 2009

### diazona

Hmm... does your professor by chance have a little black goatee and an evil cackle? :rofl: Seriously though, this problem is impossible, if you assume that the acceleration is uniform. That is, there's no constant acceleration that can stop the train in a distance of 8m in a time of 3s - those two conditions are incompatible with each other. (I'll leave it for you to prove that if you want) If it's going to be done, you'd have to specify an acceleration that varies with time (of course, there's nothing in the problem to tell you how it varies).

9. Dec 23, 2009

### fireemblem13

more like a bald russian with a difficult to understand accent

10. Dec 23, 2009

### cepheid

Staff Emeritus
Yeah, that is a nasty question. I guess that is why they are bonus questions. I should point out, though, that in neither case is it very clear what you have to do.

11. Dec 23, 2009