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

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Answer

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

Steps

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

Step 2 ：Integrating $v (t) = 3 t^{2}$ 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 $s (t) = t^{3} + 6$ .