Identifying Increasing Speed from Position vs. Time Graphs

In summary, the graphs show the position of three objects plotted as a function of time. The velocity of the object increases when the slope of the distance vs. time graph is increasing. Therefore, the correct answer is graph III.
  • #1
Beanie
32
0

Homework Statement


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)

Homework Equations

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.
 

Attachments

  • Screen Shot 2015-08-15 at 1.56.08 PM.png
    Screen Shot 2015-08-15 at 1.56.08 PM.png
    1.9 KB · Views: 867
Last edited:
Physics news on Phys.org
  • #2
I don't see an attempt. What do you think?
 
  • #3
brainpushups said:
I don't see an attempt. What do you think?
I initially thought that the answer was graphs I and II
 
  • #4
Beanie said:
I initially thought that the answer was graphs I and II

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.
 

Attachments

  • upload_2015-8-15_16-5-41.png
    upload_2015-8-15_16-5-41.png
    1.1 KB · Views: 541
  • #5
brainpushups said:
Why?

I thought the correct answer was graphs 1 and 2 because the distance in graphs 1 and 2 changes over time. Therefore, the velocity must be increasing over time.
 
  • #6
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
brainpushups said:
Sorry, I meant to write graphs 1 and 3 instead of graphs 1 and 2. I was thinking along the lines that if distance is changing, velocity must be increasing. But I realize now that that is not necessarily true because the object could be changing positions with a constant velocity. So how can I know whether velocity is increasing or not by looking at a distance vs. time graph?
 
  • #8
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
brainpushups said:
In the situation you gave, the graph would look like an upwards slope, like graph 1. The slope of the line represents that as time goes on the distance traveled increases.
 
  • #10
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
brainpushups said:
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?

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
Beanie said:
So just to recap, the slope of a distance vs. time graph is m/s, and therefore velocity

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.

Beanie said:
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.

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.

Beanie said:
So the correct answer is graph III?

Yes.
 
  • #13
brainpushups said:
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.

Thank you!
 

1. What is a position vs. time graph?

A position vs. time graph is a visual representation of an object's position over a period of time. The position is shown on the y-axis and time is shown on the x-axis. It is commonly used to analyze the motion of an object and can provide information about its velocity and acceleration.

2. How do you interpret a position vs. time graph?

To interpret a position vs. time graph, you can look at the slope of the line. A steeper slope indicates a greater velocity, while a flat line indicates no movement. The direction of the slope also indicates the direction of the object's motion. Additionally, the shape of the curve can provide information about the object's acceleration.

3. What does a horizontal line on a position vs. time graph represent?

A horizontal line on a position vs. time graph represents an object at rest. This means that the position of the object is not changing over time, and therefore, the velocity and acceleration are both zero.

4. How can you use a position vs. time graph to calculate velocity?

To calculate velocity from a position vs. time graph, you can use the slope formula: velocity = change in position/change in time. This means that the velocity is equal to the rise over run of the line on the graph. You can also find the average velocity by finding the slope of a line connecting two points on the graph.

5. What is the difference between a positive and negative slope on a position vs. time graph?

A positive slope on a position vs. time graph indicates that the object is moving in the positive direction (e.g. up, right, forward) and a negative slope indicates that the object is moving in the negative direction (e.g. down, left, backward). This is because the slope is calculated by dividing the change in position by the change in time, and a positive change in position results in a positive slope, while a negative change in position results in a negative slope.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
206
  • Introductory Physics Homework Help
Replies
3
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
197
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
917
  • Introductory Physics Homework Help
Replies
19
Views
856
  • Introductory Physics Homework Help
Replies
1
Views
691
Back
Top