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hey guys it's Roy and today I'm going to

teach you how to derive the final

velocity formula this is working off the

assumption that the final equals V

initial plus acceleration times time and

this we went over in a previous video

about acceleration so if we have this

equation and we square both sides we get

V squared + V by itself just means final

velocity equals initial velocity plus

acceleration times time all of this

squared now if we were to spread this

out if we were to multiply it out we

would get initial velocity squared plus

2 times initial velocity times

acceleration times time plus

acceleration squared times x squared now

what we're going to do is we are going

to take out we're going to factor out 2

and acceleration and accelerations over

here and then we'll just have to divide

this by 2 in order to factor out the 2

so this equals initial velocity squared

plus 2 times acceleration times initial

velocity times time plus acceleration

times x squared over 2 and we still have

acceleration in there because this is

acceleration squared so when we factor

out one acceleration we still have one

left

and then we have to divide by 2 because

we're factoring out 2 now what does this

look like right here if you go back to

the final position equation you can see

that this is actually the formula for

change and displacement and the reason

we don't have initial displacement over

here is because that wouldn't make it a

change in displacement that would make

it a final position therefore this

formula right here is a change in

displacement based on both velocity and

acceleration therefore we have a final

equation down here of V squared and this

is again final velocity equals initial

velocity squared

plus two times acceleration times change

in position and this is one of the most

important equations in mechanics and

kinematics and therefore we want to

remember this and use in the future