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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
