A particle moves in a \(3\)-dimensional space so that its acceleration vector at any time \(t>0\) is \( \boldsymbol{a}(t) = \boldsymbol{i} + 2\ \boldsymbol{j} \) and its initial velocity is \( \boldsymbol{v}(0) = \boldsymbol{k}\). If \(S\) is the speed of the particle at \(t = 2\), what is the value of \(S^2\)?

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