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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