Distance-Time Graphs: Negative Gradient Explained

[KellyOsbourne]

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!

 

[Hootenanny]

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.

 

[KellyOsbourne]

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 :)

 

[Hootenanny]

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?

 

[KellyOsbourne]

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.