Displacment vs Distance - Area under the graph.

[Lunasly]

Hello everyone,

The area under a velocity/time graph represents displacement or distance? It has always been to my knowledge that the area on the curve that is above the x axis is a positive displacement and the area under the graph that is below the x-axis is a negative displacement. Thus, if the area on the curve above and below the x-axis where the same, then the net displacement would be 0.

Just looked in the back of EK and it says that the are asunder the curve represents distance and not displacement because the area below the x-axis is regarded as positive.

Help?

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[chiddler]

Hello everyone,

The area under a velocity/time graph represents displacement or distance? It has always been to my knowledge that the area on the curve that is above the x axis is a positive displacement and the area under the graph that is below the x-axis is a negative displacement. Thus, if the area on the curve above and below the x-axis where the same, then the net displacement would be 0.

Just looked in the back of EK and it says that the are asunder the curve represents distance and not displacement because the area below the x-axis is regarded as positive.

Help?

Integral of velocity is distance. Integral of acceleration is velocity. Yes.

You can find distance or displacement from such a graph. If you want distance, it's absolute value of everything so you treat everything as positive. It's like if you walk forward two meters and walk backwards the same distance. Distance is four, displacement is zero.

But i'm not sure i'm understanding your question. does this address it?

 

[Lunasly]

My question basically is that EK says that the area under the graph of a velocity time graph is distance and NOT displacement. It makes sense that you can find distance (treat everything as a positive) and displacement. However, why does EK say otherwise?

 

[milski]

EK is correct if you treat the area as strictly geometric area, which is always positive. If you treat it as an integral where the area under the x axis is taken with negative sign, it will be a displacement.


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[Lunasly]

So the area under the curve can be seen as both displacement and distance depending on how you treat the data; that is, the area under the curve if treated as geometric area (thus all positive) will be seen as distance regardless of whether the area under the curve is below or above the x-axis. However, the area under the curve if treated as an integral will be seen as displacement since the area under the curve above the x-axis is positive while the area under the curve below the x-axis is negative.

Right? If this is the case, then EK is technically wrong as they should have had an answer that said both distance AND displacement. However, you had to choose one of the two as an answer choice.

 

[milski]

Your summary is correct.

As for EK being right or wrong - it becomes a matter of phrasing. If the question is about area, I'd probably go with distance, since area is something that normally would not be negative.