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In summary: No problem, thanks for letting me know.In summary, the forum software has a trim option to prevent posts from being oversized.

- #1

bloodhound

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Hi,

I am reading through a study guide and currently going through the kinematics section.

In the section on uniform acceleration it gives all the standard formulae and explains how they are derived.

It says that average velocity = s/t, but also that it is equal to (v+u)/2 if the average velocity is uniform.

Can someone explain this second part to me please? I understand the concept of averages and that we are dividing by 2 because we are only using 2 values, v and u. But through explaining the concept how does adding together v and u bring us the average velocity?

Thanks.

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- #2

Doc Al

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How about this:

v = u + at (or: at = v - u)

s = ut + 1/2at^2

ave velocity = s/t = (ut + 1/2at^2)/t = u + 1/2at = u + 1/2(v - u) = (v+u)/2.

- #3

bloodhound

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Doc Al said:

How about this:

v = u + at (or: at = v - u)s = ut + 1/2at^2

ave velocity = s/t = (ut + 1/2at^2)/t = u + 1/2at = u + 1/2(v - u) = (v+u)/2.

Yes that makes sense, thanks.

However in the book, it seems like it is saying that through a common sense approach this can be explained; i.e. not through using the other formulae.

Here is how it is written in the book:

- #4

Phrak

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Does the forum software have a trim option to prevent this?

- #5

bloodhound

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It is the 3rd picture which contains the sentence that is causing me grief.

It says 'Since the velocity is changing uniformly we know that this average velocity must be given by:

average velocity = (v+u)2.

Without using the other equations of uniform motion, why is this the case, why must it be given by (v+u)/2?

- #6

bloodhound

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Phrak said:

Does the forum software have a trim option to prevent this?

To prevent what?

- #7

Doc Al

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bloodhound said:

However in the book, it seems like it is saying that through a common sense approach this can be explained; i.e. not through using the other formulae.

There's nothing wrong with that. If something varies uniformly (linearly) that reasoning is fine. For example, if a flat incline goes from a height of 5 m to 25 m, what's the average height? Right in the middle, which is (5 + 25)/2 = 15 m.

- #8

Doc Al

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Phrak said:

Does the forum software have a trim option to prevent this?

bloodhound said:

To prevent what?

To prevent oversized attachments from messing up the formatting. (Which makes the posts harder to read.)

I've seen this happen quite a bit. (I'll report it to the admins to see if there's a solution.)

Last edited:

- #9

bloodhound

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Doc Al said:

To prevent oversized attachments from messing up the formatting. (Which makes the posts harder to read.)

I've seen this happen quite a bit.

Oh right, sorry I should have reduced the size. Maybe I can edit it still?

## FAQ: Why is average velocity=(v+u)/2

## 1. Why is the average velocity formula (v+u)/2?

The average velocity formula (v+u)/2 is derived from the definition of average velocity, which is the total displacement divided by the total time taken. In this case, the total displacement is represented by (v-u) and the total time taken is 2t, where t is the time taken to cover the distance between the initial velocity (u) and final velocity (v). Thus, (v+u)/2 is a simplified form of (v-u)/2t, which is the average velocity formula.

## 2. Can the average velocity formula be used for non-uniform motion?

Yes, the average velocity formula can be used for non-uniform motion. It is a general formula that calculates the average velocity over a given time period, whether the motion is uniform or non-uniform. However, for non-uniform motion, the average velocity calculated may not represent the actual velocity at any specific time during the motion.

## 3. How is average velocity different from instantaneous velocity?

Average velocity is the total displacement divided by the total time taken, while instantaneous velocity is the velocity at a specific point in time. Average velocity gives an overall picture of the motion over a period of time, while instantaneous velocity gives the velocity at a specific moment.

## 4. Is average velocity the same as average speed?

No, average velocity is not the same as average speed. Average speed is the total distance traveled divided by the total time taken, while average velocity is the total displacement divided by the total time taken. Average speed does not take into account the direction of motion, while average velocity does.

## 5. Can the average velocity formula be used for objects moving in different directions?

Yes, the average velocity formula can be used for objects moving in different directions. The formula takes into account the direction of motion by considering the total displacement (v-u), which includes both magnitude and direction. Therefore, the average velocity calculated will also have a direction associated with it.

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