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okay Andrew this is for you we are given
a position function of the moving
particle and we have two parts first we
are going to find the average speed from
4 to 6 and this right here is the slope
formula pretty much right so I will just
write this down right here
the average remember what you do is you
look at the final position so I just put
up this is my s ok s at 6 the final
position and then minus s o 4 because
that will be the initial position and
then T PI D PI how long it takes right
so you'll be 6 minus 4 which is 2
seconds but this is pretty much all you
have to do well to get S of 6 you refer
back to this equation and that's just
put it down here real quick
s of 6 this is equal to you put 6 into
the t's you get negative 2 times 6 to
the third power and we add 13 T squared
so that's plus 13 and the T is 6 so for
the 6 here and then we have that squared
of course right here you can just work
this out if that's you you end up with
36 and then similarly we calculate s off
work by putting the 4 into all the T's
right here so we end up with negative 2
times 4 to the 3rd power plus 13 times 4
to the second power and you end up with
80 well we all right here we can come
back as of 6 is 36 and then we - as of 4
which is 80 and over that's just QA 6
minus 4 which is of course 2 but just do
this on your own on the table is
negative 44 on the bottoms tools all
together you end up with negative 22
right there's negative 44 divided up 2
divided by 2 so negative 22 and notice
the S which is the position is in meters
at an teasing second so right here I
will write it down as meters per second
but let me spell D orbitals sometimes if
you abbreviated as as second word
positions
seconds right yeah
so that's it and here you have negative
velocity and it means um you know I'm
average moving toward the left alright
on the other hand if you want to find
the instantaneous velocity of the moving
particle 20 is 4 we had to do some
calculus named you can just do the
derivative because the first derivative
tells you the instantaneous velocity
alright so right there I will just write
down v of T which is just the derivative
of the position function well if you
look here here you can just bring the
street to the front and you have
negative 6t and the minus 1 to the power
so we have the square here and then we
add bring the 2 to the front which is
going to be 26 T to the first power so
that's pretty much the idea right so
this is V of T and then to get V of 4
same thing pretty much just plug in 4
into although T so we can just get
negative 6 times 4 squared plus 26 times
4 like this work this out in the end you
end up with 8 and once again this is the
instantaneous velocity and the unit for
this is meters per second after one
second second like this right so this
right here yes yeah this right here is
it and
![Instantaneous Velocity in Physics - Formula, Definition & Examples - [1-2-5]](https://i.ytimg.com/vi/6FAFVkl66i4/mqdefault.jpg)
