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Kampret

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## Homework Statement

acceleration of certain oscillating particle described by a = -x/9 determine the position of this particle when t = 3π/2

if when t=0 x=0 and v=v0

## Homework Equations

dv/dt=a

## The Attempt at a Solution

frankly im not sure how to start but i have two ways in my mind(even i doubt both of them) the first is using

dx/dx dv/dt=a

dx/dx dv/dt = -x/9

v dv = -x²/18

v²=-x²/9 but after this im cant go any futher since v = √(-x²/9) and √(-) is impossible

so my second attempt is

dv/dt=a

dv/dt=-x/9

dv=-x/9dt

integrating both sides(i doubt this one is correct because x is somewhat have t fraction within it and it different than some unrelated variable. so im not sure about this one)

v=-xt/9+c (here im also dont understand since in the problem just written when t =0 x=0 ←exact value so it help me determine the c of x but v=v0 so ?im cant understand this) if i try insert t by 0, v0 = c which i dont know exact value for both sides so i just go with when t=0 v=0 so the c value is zero even though i fully understand that VERY different between v=0 and v0

but i just confuse!

so since c=0 v become =-xt/9

and x is

dx/dt=-xt/9 and

dx/x=-t/9dt

ln x = -t²/18+c

but i i know i cant do anything after this since if if i subsitute x with 0 ln0 is absurd

at last im hope someone can help me with this problem,im know this one (my attempt) was very messy until to the point it embarrassing for me to post this so i beg once again please how the correct method to solve this problem

ps:for delta² or sammys if by any chance both of you see this post please help me

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