Find $s(t)$, where $s(t)$ represents the position function, $v(t)$ represents the velocity function, and a(t) represents the acceleration function.
$$a(t)=-6t+2\text{, with }v(0)=2\text{ and }s(0)=9$$
$$s(t)=$$

Step 1 ：Given the acceleration function $a(t)=-6t+2$.

Step 2 ：The velocity function $v(t)$ is the integral of the acceleration function. Integrate $a(t)$ to get $v(t)=-3t^2+2t+C_1$.

Step 3 ：Given the initial condition $v(0)=2$, substitute into the velocity function to solve for $C_1$. This gives $C_1=2$.

Step 4 ：So the velocity function is $v(t)=-3t^2+2t+2$.

Step 5 ：The position function $s(t)$ is the integral of the velocity function. Integrate $v(t)$ to get $s(t)=-t^3+t^2+2t+C_2$.

Step 6 ：Given the initial condition $s(0)=9$, substitute into the position function to solve for $C_2$. This gives $C_2=9$.

Step 7 ：So the position function is $s(t)=-t^3+t^2+2t+9$.

Step 8 ：$\boxed{{\displaystyle s(t)=-t^3+t^2+2t+9}}$ is the final answer.