Position vs. Time Graphs

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1. Aug 15, 2015

Beanie

1. The problem statement, all variables and given/known data
Three objects can only move along a straight, level path. The graphs below show the po- sition d of each of the objects plotted as a function of time t.

The magnitude of the velocity ∥⃗v∥ of the object increases in which of the cases? (view image/attached file)

2. Relevant equations

3. The attempt at a solution
I thought the correct answer was graphs 1 and 3 because the distance in graphs 1 and 3 changes over time. Therefore, the velocity must be increasing over time. However this answer is not correct.

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Last edited: Aug 15, 2015
2. Aug 15, 2015

brainpushups

I don't see an attempt. What do you think?

3. Aug 15, 2015

Beanie

I initially thought that the answer was graphs I and II

4. Aug 15, 2015

brainpushups

Why?

Edit:
Sorry about the attachment; accidentally hit paste and there was an image in my clipboard. Couldn't figure out how to delete the attachment.

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5. Aug 15, 2015

Beanie

6. Aug 15, 2015

brainpushups

Actually the distance does NOT change in graph II. If it did then there would need to be some variation in the vertical direction (y direction of the axes).

One quick point: The question asks about changing speed, not changing distance.

Let me ask you this: is it possible to be in motion without changing your speed?

Edit: for clarity

7. Aug 15, 2015

Beanie

8. Aug 15, 2015

brainpushups

Two questions:

Suppose you are moving 2 meters per second. What would the distance vs time graph of this motion look like? If you are unsure, then calculate the distance for a couple of different times (1 second, 2 seconds, etc) and make a chart then sketch the graph.

What does the slope of the line you just sketched represent?

9. Aug 15, 2015

Beanie

10. Aug 15, 2015

brainpushups

Indeed. The graph is a straight line with positive slope. And while you are not incorrect about how you stated the meaning of slope there is a more eloquent way of expressing what the slope represents. Check out the units of the slope - you should notice that they are units of velocity (rise/run = m/s in the example I gave you). So... the slope of the distance vs. time graph is equal to the velocity.

If the slope of the curve on a distance vs. time graph represents the velocity and you are asked to identify cases in which the velocity is changing then you need to find the graph for which the slope is not constant. Does that make sense?

11. Aug 15, 2015

Beanie

Yes, thank you. This makes much more sense.

So just to recap, the slope of a distance vs. time graph is m/s, and therefore velocity. So when it asks for a graph where the velocity is increasing, I must find a graph where the velocity is not constant, meaning the slope is not constant.

So the correct answer is graph III?

12. Aug 15, 2015

brainpushups

The slope of the distance vs. time graph will have units of distance/time. For the particular example I gave the units were m/s, but they could just as easily be km/h.

You are asked to identify a graph for which the object's speed is increasing so you need to find a graph of distance vs. time for which the slope is increasing.

Yes.

13. Aug 15, 2015

Thank you!