## Displacement or position?

[22 Jan 2007]

Ewen, a visitor to the Interactive Mathematics site, writes:

On your displacement-time graph, it is more correct to title the vertical axis “position”. From the vertical axis, you can then calculate the “displacement” by simply subtracting one position from another between any two times. It’s like labelling the horizontal axis “time interval” rather than just “time”. You’re not the first to make this mistake. I’ve seen it in a few textbooks. (But, they’re usual textbooks for lower grades, or lower levels of Physics. If that’s why you’ve done it, then I understand.)

I believe the term “displacement” is used correctly here. At the top of the page, the first graph correctly uses “distance” to describe the total length of the journey. For the graphs under the heading “Displacement-time graphs”, the axis description “displacement” is used correctly to indicate “how far from the origin we are at that time”.

In the introduction to the Kinematics chapter, I state:

“Distance” normally refers to the total distance an object moves during a particular journey.

“Displacement” refers to the distance from the starting point at a particular instant in time.

Wikipedia says displacement…

“…specifies the position of a point or a particle in reference to an origin”

I’m not sure that “position” adequately describes what we mean. If it was something like “position in km from the origin” maybe, but it would be better as “distance from the origin” which is really “displacement” anyway.

Anyone like to weigh in on this?

### 6 Comments on “Displacement or position?”

1. Harro! says:

Hi Squares…

What’s this site about? Marketing Mathematics?
We’ve listed you…. http://www.harro.com

2. Murray says:

Well, thanks, Harro!

3. Alan Cooper says:

I’m with you on the graphs. This is one of those situations where there is not a unique accepted usage and so we should not pretend there is. But I do prefer “displacement” to “position”.

In fact, to determine a coordinate, both words need to be modified by including reference to the origin (as well as unit of measurement), but to use the single word “displacement” rather than “displacement from the origin” is in my opinion less misleading. This is because even if the origin is not mentioned the use of the word “displacement” implies that it must be from something, whereas the word “position” stands alone to identify a point without begging the question “relative to what?”. (In fact the same position can be described by different displacements depending on where we put our origin.)

Where I don’t quite agree with you is on that kinematics page. The distinction between displacement and distance is just that displacement has a direction whereas distance does not, and I don’t really think that it is any less common to refer to a net or final displacement or a distance at time t than the other way around.

4. Murray says:

On your last paragraph, I don’t know that I have ever heard the expressions “net displacement” or “displacement travelled”.

The displacement from the origin can be zero for a journey (we ended up where we started) or it can even be negative (since it has a direction), but the distance travelled will always be some positive value.

“Net distance travelled” or “net distance” makes more sense, surely?

5. Ewen says:

Consider 2 more arguments for naming the vertical axis “position” rather than “displacement”. The first is that if you were to use the numbers to calculate the displacement between any 2 times, you would substitute them into the formula: displacement equals position 2 subtract position 1 (not displacement 2 subtract displacement 1). The second is that when you plot the graph you are plotting positions, not displacements.
Because of these arguments, I’d also prefer to make the title of the graph “position vs. time” rather than “displacement vs. time”.

6. Li-sa says:

Displacement is a vector. Position – a point.
Displacement: change in position.

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