Question

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Answer 1

`s(t)=-t^3+3t^2+t+10`

Explanation:

The position is found by taking the antiderivative of velocity. Velocity is found by taking the antiderivative of acceleration. So:

`a(t)=-6t+6\\v(t)=\int -6t+6 dt\\v(t)=-3t^2+6t+C\\v(0)=-3(0)^2+6(0)+C=1\\C=1\\v(t)=-3t^2+6t+1\\s(t)=\int -3t^2+6t+1dt\\s(t)=-t^3+3t^2+t+C\\s(0)=-(0)^3+3(0)^2+0+C=10\\C=10\\s(t)=-t^3+3t^2+t+10`