# a particle moves along an s-axis. use the given information to find the position function of the particle: `a(t)=12sin12t` ; `v(0)=12` ; `s(0)=12`

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Expert Answers

jeew-m | Certified Educator

Let us say the velocity function is v(t) and position function is s(t).

`a(t) = (dv(t))/(dt)`

`dv(t) = a(t)dt`

`v(t) = inta(t)dt`

`v(t) = int12sin12tdt`

`v(t) = -cos12t+C` where C is a constant.

`v(0) = -cos(12xx0)+C`

`12 = -1+C`

`C = 13`

`v(t) = -cos12t+13`

`v(t) = (ds(t))/(dt)`

`s(t) = intv(t)dt`

`s(t) = int(-cos12t+13)dt`

`s(t) = -(sin(12t))/12+13t+D`

`s(0) = D`

`D = 12`

`s(t) = -(sin12t)/12+13t+12`

** So the position function is **`s(t) = -(sin12t)/12+13t+12`