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

Answer

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Answer

Therefore, the position function is $s(t) = t^3 + 6$.

Steps

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 $s(t) = t^3 + 6$.