# Velocity and Acceleration

A particle moves in a \(3\)-dimensional space so that its acceleration vector at any time \(t>0\) is \( \boldsymbol{a}(t) = -4\ \boldsymbol{i} -6t\ \boldsymbol{j}+12t\ \boldsymbol{k} \), initial velocity is \( \boldsymbol{v}(0) = 0\), and initial point is \(\boldsymbol{r}(0) = \boldsymbol{j}-2\ \boldsymbol{k}\). The position vector at \(t = 4\) is represented by \(\boldsymbol{r}(4) = a\ \boldsymbol{i} + b\ \boldsymbol{j} + c\ \boldsymbol{k}\). What is the value of \(a+b+c\)?

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