# Velocity and Acceleration

Level pending

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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