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

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Detailed Solution

$\vec{a} = \frac{\vec{F}}{m} = \frac{2 \hat{i} + 3 \hat{j} + 5 \hat{k}}{2}, {\vec{r}}_{f} - {\vec{r}}_{i} = \vec{u} t + \frac{1}{2} \vec{a} t^{2}$

${\vec{r}}_{f} - (0 \hat{i} + 0 \hat{j} + 0 \hat{k}) = \frac{1}{2} \times (\frac{2 \hat{i} + 3 \hat{j} + 5 \hat{k}}{2}) {(4)}^{2}$

${\vec{r}}_{f} = 8 \hat{i} + 12 \hat{j} + 20 \hat{k} \Rightarrow b = 12$

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