A body of mass 2 kg moves under a force of $$\left(2\hat{i} + 3\hat{j} + 5\hat{k}\right)$$ N. It starts from rest and was at the origin initially. After 4 s, its new coordinates are $$(8, b, 20)$$. The value of $$b$$ is ________. (Round off to the Nearest Integer)

The body of mass $$m = 2$$ kg starts from rest at the origin and moves under a constant force $$\vec{F} = 2\hat{i} + 3\hat{j} + 5\hat{k}$$ N.

The acceleration is $$\vec{a} = \frac{\vec{F}}{m} = \frac{2\hat{i} + 3\hat{j} + 5\hat{k}}{2} = 1\hat{i} + 1.5\hat{j} + 2.5\hat{k}$$ m/s$$^2$$.

Since the body starts from rest at the origin, the displacement at time $$t$$ is $$\vec{s} = \frac{1}{2}\vec{a}t^2$$.

At $$t = 4$$ s: $$\vec{s} = \frac{1}{2}(1\hat{i} + 1.5\hat{j} + 2.5\hat{k})(16) = 8\hat{i} + 12\hat{j} + 20\hat{k}$$.

The coordinates are $$(8, 12, 20)$$. Comparing with the given coordinates $$(8, b, 20)$$, we find $$b = 12$$.