# Velocity (Where did I go wrong?)

#### ldv1452

Velocity is a basic concept that I thought I understood well, but perhaps I am missing something here. My professor gave me an explanation but am I still unclear.

If you run a complete loop around an outdoor track (400m) and then an additonal 300 m in 200s (total time), your average velocity is what?

My response was 0.5 m/s, but the correct answer was said to be 1.5 m/s.

My thinking was that by going 300m you would end up 100m away from the start and velocity (depending on displacement) would give my answer. I was told that I shouldn't look at this as a two dimensional loop, but rather look at it one dimensionally and count 300m as the total displacement, rather than 100. Can someone please clarify this for me?

Thank you

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#### Kittel Knight

Of course, 400m + 300m = 700m
So, if you run 700m in 200s (total time), your average velocity is what?

#### brocks

My response was 0.5 m/s, but the correct answer was said to be 1.5 m/s.

I think your logic is correct. The prof is right if the extra 300m is in a straight line from the starting line, but I never saw a track like that.

#### brocks

Of course, 400m + 300m = 700m
So, if you run 700m in 200s (total time), your average velocity is what?
Unknown, unless the starting and finishing positions are given. You might be thinking of average speed.

#### olivermsun

If you end the 400 m loop with the front straightaway, then after the first 300 m you'd end up 100 m behind the start. So, it seems as if the avg. velocity was -0.5 m/s!

#### nonequilibrium

I think neither answers make much sense.

What the professor is about just makes no sense, even if you have a one-dimensional track, because even on a one-dimensional track you have to return at some point and there's no indication that you haven't started returning during those 300m, in which case the displacement wouldn't be 300m.

And your reasoning assumes that the amount of track left to complete the loop (100m, as you say) is the same as the displacement, but that's only the case if those 100m are on a straight line! (take for example a circular track, and say you start at the bottom, then at the end you'll be at 3 o'clock, and the circular arc to the bottom has length 100m, but the actual total displacement is obviously less)

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#### ldv1452

I think neither answers make much sense.

What the professor is about just makes no sense, even if you have a one-dimensional track (which wouldn't make much sense either), because even on a one-dimensional track you have to return at some point and there's no indication that you haven't started returning during those 300m, in which case the displacement wouldn't be 300m.

And your reasoning assumes that the amount of track left to complete the loop (100m, as you say) is the same as the displacement, but that's only the case if those 100m are on a straight line! (take for example a circular track, and say you start at the bottom, then at the end you'll be at 3 o'clock, and the circular arc to the bottom has length 100m, but the actual total displacement is obviously less)
I know what you're saying here and I was thinking the same thing (if we want to be completely accurate). It appeared to me though that the question was to test the understanding between average speed and average velocity, which is why I took 100m to be the displacement (or possibly -100m and end up with -0.5m/s, as another poster suggested).

#### ldv1452

I don't mind losing the points on the test, what really frustrated me is that he seemed annoyed I even questioned it and when I tried to challenege his explanation and give my reasoning he didn't even let me really go through it. He just said ok you challenged me and i gave you my answer so we're done. I've never had a professor that behaved this way.

#### olivermsun

Well I mean, I guess if you define it to be a 1-d circular world, then okay, for the circular track where 300 m = -100 m (they are the same position), you could say the velocity is correctly 1.5 m/s = -0.5 m/s.

But this doesn't sound like the only reasonable interpretation given the problem as stated in the OP.

"I gave you my answer so we're done" doesn't sound like the best way to teach imho.

#### ldv1452

Some thought the same as me. Many actually got the question right though, but only because they didn't even think that going around the track they'd actually end up closer after 300m (see that's what I thought the "trick" to the problem was....to recognize the final displacement). He used the fact that many or most students got it right as support why my thinking must be wrong.

#### ldv1452

It is what it is I guess. I just wanted to make sure my thinking wasn't way off base and that I wasn't missing something obvious.

#### brocks

And your reasoning assumes that the amount of track left to complete the loop (100m, as you say) is the same as the displacement, but that's only the case if those 100m are on a straight line!
Most tracks are not circular. They have about 110m straight sides, with about 90m curves on each end.

#### brocks

It is what it is I guess. I just wanted to make sure my thinking wasn't way off base and that I wasn't missing something obvious.
You missed the fact that your prof is a jerk, but it's too late to do anything about that now. Keep your head down, and try to avoid taking any more classes from him.

#### ldv1452

You missed the fact that your prof is a jerk, but it's too late to do anything about that now. Keep your head down, and try to avoid taking any more classes from him.
Haha, yeah I did my venting earlier, but I am considering talking to the physics dept head or at least another professor about this. It may be a waste of time, but it doesn't seem right to treat a student this way.

#### nonequilibrium

Hm, he still has to grade your exam though, so watch out. Anyway, it might be better to bring it up with the professor himself, before dissing him to other professors (although I very well understand your feelings as I've also had experience with unjust treatment; in my case I let it slide, but I did decide to avoid all courses of his; doesn't mean you should let it slide, by all means!)

#### brocks

Haha, yeah I did my venting earlier, but I am considering talking to the physics dept head or at least another professor about this. It may be a waste of time, but it doesn't seem right to treat a student this way.
It might be worse than a waste of time, if you are going to be taking more physics classes. There is no way it can help you to have the dept associate you with making trouble for a guy over a few points. Just give him a rotten (anonymous) evaluation at the end of the term, and move on.

#### ldv1452

It might be worse than a waste of time, if you are going to be taking more physics classes. There is no way it can help you to have the dept associate you with making trouble for a guy over a few points. Just give him a rotten (anonymous) evaluation at the end of the term, and move on.

Those are some good points. I'm sure I'll just end up letting it go. The thought crossed my mind in frustration, but I know its not worth the hassle. Thanks for the input on this!

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