Distance-Time Graphs: Negative Gradient Explained

  • Context: High School 
  • Thread starter Thread starter KellyOsbourne
  • Start date Start date
  • Tags Tags
    Graphs
Click For Summary

Discussion Overview

The discussion revolves around the interpretation of distance-time graphs, particularly the implications of a negative gradient. Participants explore the definitions of distance and displacement, the nature of speed and velocity, and the potential confusion between distance-time and position-time graphs.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion over the concept of a negative gradient in distance-time graphs, questioning how distance, defined as "the amount of ground covered," can have a negative slope.
  • Another participant asserts that a distance-time graph cannot have a negative gradient since distance is a scalar quantity, while a position-time graph can have a negative gradient as it represents velocity, a vector quantity.
  • A participant requests clarification on whether the graphs in question are indeed distance-time graphs or position-time graphs, suggesting that the negative gradient may indicate a misunderstanding.
  • One participant claims that the graph linked by another is incorrect, stating that a negative gradient implies negative speed, which they argue is impossible.
  • Another participant expresses relief at the clarification, indicating they thought they were misunderstanding the concepts.

Areas of Agreement / Disagreement

Participants generally agree that distance is a scalar quantity and cannot have a negative gradient, while there is contention regarding the interpretation of the graphs and whether they are distance-time or position-time graphs. The discussion remains unresolved regarding the correctness of the graph linked.

Contextual Notes

There is uncertainty regarding the definitions and distinctions between distance-time and position-time graphs, as well as the implications of negative gradients in these contexts. The discussion highlights the need for clarity in interpreting graphical representations of motion.

KellyOsbourne
Messages
3
Reaction score
0
I was told by my teacher that the definition for distance is just "the amount of ground covered", and that displacement is "the distance in a particular direction". I was looking at some distance-time graphs online and I saw that towards the later stage of the journey in some of the graphs, the gradient of the distance-time graph was negative. Their explanation for the negative gradient was that the object was moving towards the starting position. I do not understand that. Even if the object is moving towards the starting position, it is still covering "ground" and it would go up, right? And the gradient of a distance-time graph is the speed, and I didn't think there was anything called negative speed. I know about negative velocity, but negative speed? Please clear this for me! I want to know how the gradient of a distance-time graph can be negative, when distance is just the "ground" covered.

This could be a very stupid question :$ But I am sometimes very blind to the obvious. Please help! :)

Thank you a lot in advance!
 
Physics news on Phys.org
KellyOsbourne said:
I was told by my teacher that the definition for distance is just "the amount of ground covered", and that displacement is "the distance in a particular direction". I was looking at some distance-time graphs online and I saw that towards the later stage of the journey in some of the graphs, the gradient of the distance-time graph was negative. Their explanation for the negative gradient was that the object was moving towards the starting position. I do not understand that. Even if the object is moving towards the starting position, it is still covering "ground" and it would go up, right? And the gradient of a distance-time graph is the speed, and I didn't think there was anything called negative speed. I know about negative velocity, but negative speed? Please clear this for me! I want to know how the gradient of a distance-time graph can be negative, when distance is just the "ground" covered.

This could be a very stupid question :$ But I am sometimes very blind to the obvious. Please help! :)

Thank you a lot in advance!
Welcome to Physics Forums.

I distance-time graph cannot have a negative gradient, since as you say distance (and hence speed) is a scalar quantity. However, a position/displacement time graph can have a negative gradient since position/displacement is a vector quantity.

On a distance-time graph the gradient represents the speed, which is always non-negative. However, on a position-time graph, the gradient represents the velocity, which can be negative.

Could you provide a link to the graphs with the negative gradient, I have a sneaking suspicion that they are position-time graphs.
 
Hootenanny said:
Welcome to Physics Forums.

I distance-time graph cannot have a negative gradient, since as you say distance (and hence speed) is a scalar quantity. However, a position/displacement time graph can have a negative gradient since position/displacement is a vector quantity.

On a distance-time graph the gradient represents the speed, which is always non-negative. However, on a position-time graph, the gradient represents the velocity, which can be negative.

Could you provide a link to the graphs with the negative gradient, I have a sneaking suspicion that they are position-time graphs.

Thank you so much! Yes, that's what I thought :)
Here is the link:
http://www.golfranger.co.uk/speed.html

Please tell me if I made a mistake in interpreting whether it was a distance-time graph or a displacement-time graph, and how I can distinguish between the two.
Again, thanks so much :)
 
Last edited by a moderator:
KellyOsbourne said:
Thank you so much! Yes, that's what I thought :)
Here is the link:
http://www.golfranger.co.uk/speed.html

Please tell me if I made a mistake in interpreting whether it was a distance-time graph or a displacement-time graph, and how I can distinguish between the two.
Again, thanks so much :)
The graph shown on that page is clearly incorrect. The negative gradient of the red curve indicates a negative speed, which is impossible.

Is your school hosting this website?
 
Last edited by a moderator:
Hootenanny said:
The graph shown on that page is clearly incorrect. The negative gradient of the red curve indicates a negative speed, which is impossible.

Is your school hosting this website?

Thank you, I thought I was going bonkers!
Umm, no, my school's not hosting it. I just ran across it when I was looking for information to prepare a poster for school.
 

Similar threads

Voltage vs Distance graph for a given E vs D graph
  • · Replies 9 ·
Replies
9
Views
1K
High School Speed is distance multiplied by time -- Is this correct?
  • · Replies 9 ·
Replies
9
Views
1K
Graduate Expressing Elliptic Orbitals As Speed Functions.
  • · Replies 2 ·
Replies
2
Views
1K
Why would this be accelerating positively?
  • · Replies 6 ·
Replies
6
Views
1K
High School Acceleration of Moving Particles: Explained
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Please Explain Elementary Physics Elevator Question
  • · Replies 22 ·
Replies
22
Views
1K
Undergrad Work Done/Energy Transferred in One Dimensional Collision
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Position vs. time graph and the derivative
  • · Replies 5 ·
Replies
5
Views
3K
High School How does wind affect a turn for an aircraft?
  • · Replies 16 ·
Replies
16
Views
3K
Graph of time vs distance for sizing a motor for linear motion
  • · Replies 5 ·
Replies
5
Views
2K