# Particle in 3-D

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 \(S^2\)?