# `a(t) = 2t + 1, s(0) = 3, v(0) = -2` A particle is moving with the given data. Find the position of the particle.

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### 1 Answer

`a(t)=2t+1`

`a(t)=v'(t)`

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

`v(t)=int(2t+1)dt`

`v(t)=2(t^2/2)+t+c_1`

`v(t)=t^2+t+c_1`

Now let's find constant c_1 given v(0)=-2

`v(0)=-2=0^2+0+c_1`

`c_1=-2`

`:.v(t)=t^2+t-2`

`v(t)=s'(t)`

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

`s(t)=int(t^2+t-2)dt`

`s(t)=t^3/3+t^2/2-2t+c_2`

Now let's find constant c_2 given s(0)=3,

`s(0)=3=0^3/3+0^2/2-2(0)+c_2`

`c_2=3`

`:.` position of the particle is given by `s(t)=t^3/3+t^2/2-2t+3`