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

[bloodhound]

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.

 

[Doc Al]

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.

 

[bloodhound]

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:

 

[Phrak]

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

 

[bloodhound]

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?

 

[bloodhound]

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

To prevent what?

 

[Doc Al]

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.

 

[Doc Al]

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

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.)

 

[bloodhound]

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?