How does acceleration= final velocity - initial velocity divided by time work?

[JayJohn85]

Sorry I can't get latex working so bear with me as I am new to it. I start A-level physics in a week and during my own research I have come across something that confuses me.

Acceleration= Final velocity - Initial velocity divided by time.

What is confusing me is when your deriving other equations from this you get

at=v - u
Multiply both sides by t gives at=v-u. This confuses me cause I would get something like this

at=vt - ut

So I substituted some values into see if at=v - u works.

Acceleration= 10 m/sec^2
Time= 2 seconds
Final velocity= 20 m/s
Initial velocity= 10 m/s

10*2= 20
20-10=10
? 20 does not equal 10 so how does at=v - u work?

Doing it my way I got at= vt - ut
20*2= 40
10*2= 20
40-20= 20
at=vt - ut

Then I thought about cancelling the time term for some reason and I got
10
20-10= 10
a= v - u

Probably being really stupid here and need to go over my rudimentary algebra. Ignore this I got it acceleration is actually 5 I didnt use the equation at the start right

 

[AlephZero]

So I substituted some values into see if at=v - u works.

Acceleration= 10 m/sec^2
Time= 2 seconds
Final velocity= 20 m/s
Initial velocity= 10 m/s

Those numbers are inconsistent. with each other Either the acceleration should be 5 m/sec^2, or the final velocity should be 30 m/s, or something else is wrong.

The equations you stated is correct (for the average acceleration, or if the acceleration is constant):
a = (v - u)/t

Multiplying by t you get
at = v - u