# What is the meaning behind multiplication in physics?

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What is the meaning behind multiplication in physics? Is multiplication in physics purely mathematical or there is a physical explanation to it? How do we explain the product for example, s=v.t? Is there any meaning behind this? For example, I can say that "Distance is defined as the product of velocity 'times' time"? But what does this even mean?

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I think it "means" multiplication. So for example, if v = 1 metre/second then after 1 second the distance will be 1 metre, after 2 seconds it will be 2 metres, and so on. So the distance increases with elapsed time: it is the product of the speed and time.

!

Moderator Note

Moved to Physics (wasn't sure if it should be there or Mathematics, or maybe even Philosophy. But not Education, anyway.)

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Can you give an example with a figure?

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Posted (edited)
46 minutes ago, XVV said:

What is the meaning behind multiplication in physics? Is multiplication in physics purely mathematical or there is a physical explanation to it?

Multiplication is a term with a very wide scope in both Mathematics and Physics, where it means (in both)

Multiplication is a binary operation combining two mathematical objects or physical entities to produce a defined result according to stated rules.
Binary means there are two participating objects or entities.

That wide meaning gives rise to a whole host of uses or interpretations since it depends upon the objects or entities and the rules of combination and in some cases the order in which the operation(s) are carried out.

In Mathematics we would expect the result of the multiplication to be another mathematical object
In Physics we would expect the result to be another physical entity. The nature of the physical entity give rise to both the meaning and motiviation.
But In Physics it is possible to have more than one result. For instance Force x Distance can result in a moment or energy, which are different physical entities.

Does this help?

Edited by studiot

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9 minutes ago, XVV said:

Can you give an example with a figure?

Beside this one?

27 minutes ago, Strange said:

I think it "means" multiplication. So for example, if v = 1 metre/second then after 1 second the distance will be 1 metre, after 2 seconds it will be 2 metres, and so on. So the distance increases with elapsed time: it is the product of the speed and time.

!

Or am i misinterpreting your request?

2 minutes ago, studiot said:

Multiplication is a term with a very wide scope in both Mathematics and Physics, where it means

Multiplication is a binary operation combining two mathematical objects or physical entities to produce a defined result according to stated rules.

That wide meaning gives rise to a whole host of uses or interpretations since it depends upon the objects or entities and the rules of combination and in some cases the order in which the operation(s) are carried out.

In Mathematics we would expect the result of the multiplication to be another mathenmatical object
In Physics we would expect the result to be another physical entity. The nature of the physical entity give rise to both the meaning and motiviation.
But In Physics it is possible to have more than one result. For instance Force x Distance can result in a moment or energy, which are different physical entities.

Does this help?

Well put.

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1 minute ago, J.C.MacSwell said:

Beside this one?

Or am i misinterpreting your request?

yes beside that one

3 minutes ago, studiot said:

Multiplication is a term with a very wide scope in both Mathematics and Physics, where it means

Multiplication is a binary operation combining two mathematical objects or physical entities to produce a defined result according to stated rules.

That wide meaning gives rise to a whole host of uses or interpretations since it depends upon the objects or entities and the rules of combination and in some cases the order in which the operation(s) are carried out.

In Mathematics we would expect the result of the multiplication to be another mathematical object
In Physics we would expect the result to be another physical entity. The nature of the physical entity give rise to both the meaning and motiviation.
But In Physics it is possible to have more than one result. For instance Force x Distance can result in a moment or energy, which are different physical entities.

Does this help?

yes this does help but I don't understand that for example, in s = v.t why does v+v+v+v..........t does not make a sense

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1 minute ago, XVV said:

yes beside that one

Studiot mentioned torque. So as an example 1 newton acting at right angles to a pivot point or axis one metre away gives you 1 newton metre of torque about that point.

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18 minutes ago, XVV said:

yes this does help but I don't understand that for example, in s = v.t why does v+v+v+v..........t does not make a sense

Do you know what addition is  ?

(This is not a trick question)

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Just now, studiot said:

Do you know what addition is  ?

(This is not a trick question)

yes

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Multiplication is often related to the concept of area.
But, in general, it's quite abstract.

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Posted (edited)

Can someone give an optimum interpretation of my question?

Edited by XVV

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Posted (edited)
10 minutes ago, XVV said:

yes

Good

Then you also know that multiplication is not the only operation available - The basic ones being addition, subtraction, multiplication and division.

OK so far?

Now distance and time are fundamental physical entities (there are some (a few) more mass, electric charge and so on)

Other physical entities are secondary or derived from the few basic ones -  notice I used force, moment and energy and MacSwell mentioned torque.

By derived I mean they are combinations of the basic ones, combined by using the operations listed plus perhaps powers, roots and reciprocals.
(In other words the common operations of arithmetic and algebra)

So the definition (in terms of two basic entities distance and time) is

speed (is better than velocity) = distance divided by time

Two basic entities combined to produce a secondary 'speed'.

You have one more post in the first 24 hours, don't waste it replying to me yet.

Edited by studiot

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2 minutes ago, XVV said:

Can someone give an optimum interpretion of my question?

"I am not sure what I am asking"

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12 hours ago, XVV said:

How do we explain the product for example, s=v.t? Is there any meaning behind this?

Yes, but you need to look at it in geometric terms.
You start out at some point P, and make that the origin of your coordinate system. Velocity is a vector, so you draw that onto your chart, which gives you an arrow that points from your origin  to some new point P’: P’=0+v. The factor t is a scalar, so what the multiplication v*t means is that it lengthens the vector v, keeping its origin and direction unchanged:

|s|=(0+v)*t=v*t

That is the meaning of this kind of multiplication - it lengthens a vector along the direction it points in. The resulting quantity s is then just the total length of that new vector, which physically speaking is the point you get to after travelling for a time t with velocity v, being the tip of the new arrow in your drawing.

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22 minutes ago, Markus Hanke said:

Yes, but you need to look at it in geometric terms.
You start out at some point P, and make that the origin of your coordinate system. Velocity is a vector, so you draw that onto your chart, which gives you an arrow that points from your origin  to some new point P’: P’=0+v. The factor t is a scalar, so what the multiplication v*t means is that it lengthens the vector v, keeping its origin and direction unchanged:

|s|=(0+v)*t=v*t

That is the meaning of this kind of multiplication - it lengthens a vector along the direction it points in. The resulting quantity s is then just the total length of that new vector, which physically speaking is the point you get to after travelling for a time t with velocity v, being the tip of the new arrow in your drawing.

Nice concrete description.

You can also extend the "multiplication is repeated addition" analogy to this by saying that it lays out t vectors of length v end to end.

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10 minutes ago, Strange said:

Nice concrete description.

You can also extend the "multiplication is repeated addition" analogy to this by saying that it lays out t vectors of length v end to end.

34 minutes ago, Markus Hanke said:

That is the meaning of this kind of multiplication - it lengthens a vector along the direction it points in.

So there you have different views of multiplication, but a word of caution.

Multiplication can mean enlargement.

But it can also mean reduction. This is achieved when you multiply by a fractional number (ie a number less than 1)

And you have a difficulty reconciling reduction with repeated addition.

And multiplication can also mean 'remaining the same' or no change. This is achieved by multiplication by 1 or unity.
Physicists don't usually bother with this and call it trivial, but it is vitally important in higher mathematics.

Another meaning is called 'composition' by mathematicians.
This can result in an enlargement, no change or a reduction.

For a physical example

Consider the radio or audio signal  Asin(wt)

As written the 'scaling factor', A,  changes the size but not the shape of the signal.

Multiply the wt by A first and then taking the sine changes the shape, but not the size of the signal.

(This is a good example of where the order of multiplication is important.)

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20 minutes ago, studiot said:

Multiplication can mean enlargement.

But it can also mean reduction. This is achieved when you multiply by a fractional number (ie a number less than 1)

And you have a difficulty reconciling reduction with repeated addition.

Good point. (And that is why I referred to it as an analogy)

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1 hour ago, studiot said:

And you have a difficulty reconciling reduction with repeated addition.

Interesting.  Would this also apply to the addition of negative values?

(-1) + (-1)= -2

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Posted (edited)
35 minutes ago, Dord said:

Interesting.  Would this also apply to the addition of negative values?

(-1) + (-1)= -2

Good question.

I wanted to avoid doing that at this stage because officially (mathematically) the more negative something gets the smaller it is in that -2 is less than -1

Notice that Marcus carefully ued the absolute value or modulus symbol and also talked about making the vector longer (not larger), perhaps  to avoid discussing making the vector shorter.

We do not know the mathematical ability of XVV, for instance whether he knows about the sine function or vectors so I was trying to keep it simple.

But also consider this.

A sine wave has symmetrical positive and negative parts.

But if we multiply the wave by 2, thereby doubling its size, do you consider the negative parts made smaller or larger?

Edited by studiot

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Posted (edited)
15 hours ago, XVV said:

yes this does help but I don't understand that for example, in s = v.t why does v+v+v+v..........t does not make a sense

15 hours ago, XVV said:

Can you give an example with a figure?

Hello. Not sure I understand your question but here is an attempt, also using geometry. I'll try to include your note regarding the sum v+v+v...

If you have a constant velocity v and plot a graph you could think of the distance s as the area under graph. A numerical example:

So to calculate the distance we could use multiplication 5*10=50 in this case (5 seconds of 10m/s velocity) or we could just use sum 10+10+10+10+10=50. Numerical result is the same. But I think the physical result is different.

Le's take a to take a look at the units. Velocity is m/s and time is in seconds. If we just add velocities 10+10+... We have, physically, an increase in speed from 10 m/s to 50 m/s. So for the sum to physically get the correct result, the distance, we need to include the multiplications: 10*1 + 10*1 +...=50. Or with units spelled out: 10 m/s *1s + 10 m/s *1s +...=50m.

Side note: When stating v+v+v+v... maybe you are looking for https://en.wikipedia.org/wiki/Integral ?

Edited by Ghideon

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On 5/23/2020 at 1:11 PM, studiot said:

But also consider this.

A sine wave has symmetrical positive and negative parts.

But if we multiply the wave by 2, thereby doubling its size, do you consider the negative parts made smaller or larger?

Ah, a nicely put.  Thank you.

It just goes to show the difficulties with context and meaning when using common-or-garden words or phrases that are not always sufficiently precise for their intended purpose.

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On 5/23/2020 at 4:08 PM, Ghideon said:

Hello. Not sure I understand your question but here is an attempt, also using geometry. I'll try to include your note regarding the sum v+v+v...

If you have a constant velocity v and plot a graph you could think of the distance s as the area under graph. A numerical example:

So to calculate the distance we could use multiplication 5*10=50 in this case (5 seconds of 10m/s velocity) or we could just use sum 10+10+10+10+10=50. Numerical result is the same. But I think the physical result is different.

Le's take a to take a look at the units. Velocity is m/s and time is in seconds. If we just add velocities 10+10+... We have, physically, an increase in speed from 10 m/s to 50 m/s. So for the sum to physically get the correct result, the distance, we need to include the multiplications: 10*1 + 10*1 +...=50. Or with units spelled out: 10 m/s *1s + 10 m/s *1s +...=50m.

Side note: When stating v+v+v+v... maybe you are looking for https://en.wikipedia.org/wiki/Integral ?

This answer is not the best but it is still understandable. It helps. I have got no issues with you. What I meant was ''no person online on this website can give my answer''.

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Posted (edited)
On 5/22/2020 at 4:17 PM, XVV said:

What is the meaning behind multiplication in physics? Is multiplication in physics purely mathematical or there is a physical explanation to it? How do we explain the product for example, s=v.t? Is there any meaning behind this? For example, I can say that "Distance is defined as the product of velocity 'times' time"? But what does this even mean?

You can express most things as an equivalent scenario, if that is what you are looking for.

For S = V.t:

If we measure Bill as traveling 50 meters every 10 seconds, how far would he go if he traveled for 60 seconds?

Distance = (50 meters / 10 seconds) * 60 seconds

I normally visualize the product as an intersection of two lines crossing. Something like the figure below.

Line A might be our velocity and Line B might be the time for example. Where they cross is your product.

Edited by Endy0816

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