Solve Motion Problems: Physics 1710 Train Velocity

[fireemblem13]

These are bonus problems for a Physics 1710 class.

Homework Statement

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.

Homework Equations

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.

 

[cepheid]

Hi fireemblem13, welcome to PF!

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.

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?

 

[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.

 

[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.

 

[cepheid]

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.

 

[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 isn't 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 don't really know.

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

 

[diazona]

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).

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.

 

[diazona]

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 isn't 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 don't really know.

Hmm... does your professor by chance have a little black goatee and an evil cackle? 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).

 

[fireemblem13]

more like a bald russian with a difficult to understand accent

 

[cepheid]

Hmm... does your professor by chance have a little black goatee and an evil cackle? 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).

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.

 

[fireemblem13]

I asked him about both questions.
For #3, I asked him if it's possible for the train to be of length 7m and the back of the train arrives at a distance of 8m. He responded by saying he didn't understand the question and to assume the train is a particle, an object. So, I responded that it's impossible. We'll see what he says.

For #5, I asked him about the rails, whether they run parallel or perpendicular, whether they are continuous or discrete. He responded with "Funny questions :D Hint: What is the right answer?" What am I supposed to do with that?