13200d…: “Against the sour sea”

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The starting position of a particle is given by $\vec {p}(0) =\vector {0,0,0}$ and its acceleration is described by the vector-valued function $\vec {a} (t) = \vector {-3,0,-6t}$ for $t \geq 0$ . Suppose the initial velocity is given by $\vec {v}(0) =\vector {60,10,75}$ . Find:

The velocity function: $\vec {v}(t) =\vector {\answer {-3t+60},\answer {10},\answer {-3t^2+75}}$
The speed function: $\vec {s}(t) = \answer {\sqrt {9t^4-441t^2-360t+9325}}$
The position function: $\vec {p}(t) = \vector {\answer {-3t^2/2+60t},\answer {10t},\answer {-t^3+75t}}$
The maximum $z$ -height of the particle when $t \geq 0$ : $\text {maximum height:}\quad \answer {250}$