Find $s(t)$, where $s(t)$ represents the position function and $v(t)$ represents the velocity function. \[ v(t)=3 t^{2}, s(0)=6 \] \[ s(t)= \]

Step 1 ：Given the velocity function \(v(t) = 3t^2\), we can find the position function \(s(t)\) by integrating \(v(t)\).

Step 2 ：Integrating \(v(t) = 3t^2\) with respect to \(t\) gives \(s(t) = t^3 + C\), where \(C\) is the constant of integration.

Step 3 ：We can find \(C\) by using the initial condition \(s(0) = 6\). Substituting these values into the equation gives \(6 = 0 + C\), so \(C = 6\).

Step 4 ：Therefore, the position function is \(s(t) = t^3 + 6\).