Question

a particle is moving with acceleration s''(t)=t-2 at time t=0, s(0)=0 and the velocity s'(0)=5. find the position function s (t) at time t

Answer 1

I have to hand this in REALLY soon and I really need help with this problem!

Answer 2

integrate the acceleration function TWO times!!!

Answer 3

t-2 function?

Answer 4

Yes!!!

Answer 5

ok how?

Answer 6

do i find the antiderivative of it twice?

Answer 7

Using integration. If you wanna know more you can message me but since its urgent the solution is... First integration gives you 1/2t^2-2t. Integrating again for the second time gives you 1/6t^3-t^2. That's the position function! If you differentiated it twice you will get t-2 again.

Answer 8

thanks but I kinda need to know the steps too!

Answer 9

i'm not completely understanding integration either..

Answer 10

Okay there are nearly 200 formulas for integration but to solve your problem I used one of the basic rules... \[\int\limits_{?}^{?} x^{n}dx = \frac{ 1 }{ n+1 } x^{n+1} \] .

Answer 11

ok~

Answer 12

Understood?

Answer 13

yes... but do you mind explaining alil more?

Answer 14

so whats the n?

Answer 15

n is any arbitrary power

Answer 16

ok~ so how does the t-2 fit in the equation?

Answer 17

Oh okay its a long answer to type!!! I wish I could use skype to show you.

Answer 18

haha me too. can you explain it at all?? :(

Answer 19

Okay first in integration we assume t and -2 are two functions, when you want to integrate two functions such as t-2 its the integral of t minus the integral of 2. So to integrate t itself I used the formula I showed you earlier where n is 1 in this case. The integral of 2 is 2t. So if you follow that you will get the first integral of that acceleration and if you follow the same procedure you will get the second integral which is the position function!!!

Answer 20

1/2 t^2 came from the formula?

Answer 21

Yes!!!

Answer 22

ok so what does s'(0) =0 and s'(0)=5 have to do with this problem?

Answer 23

and what is n to find the second equation? how do I know ?

Answer 24

To your first question the answer is nothing! To your second question n is 2!

Answer 25

then why is it 1/6?

Answer 26

I told you n is any arbitrary power/exponent. 2 is an exponent on t... 1/6 is a coefficient of t

Answer 27

right but how can i get 1/6? isn't it 1/3 x^3 when I plug 2 in for n?

Answer 28

I wish i could attach a video!

Answer 29

lol

Answer 30

sorry I'm not getting this.. oh well i gotta hand it in soon now...

Answer 31

Will your teacher ask how you got your answer?

Answer 32

yeah

Answer 33

I guess its too late for me to do some more explanation.

Answer 34

haha you helped me alot. thanks

Answer 35

Np

Answer 36

Hey

Answer 37

yup?

Answer 38

Did it go smoothly?