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A body of mass 2kg moves under a force of (2\widehat{i}+3\widehat{j}+5\widehat{k})N. It starts from rest and was at the origin initially. After 4s, its new coordination are (8,b,20). The value of b is _________ (Rounded off to the nearest integer)
Option: 1 12
Option: 2 13
Option: 3 14
Option: 4 15

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\begin{aligned} \overrightarrow{\mathrm{a}} &=\frac{\overrightarrow{\mathrm{F}}}{\mathrm{m}}=\frac{2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{2} \\ &=\hat{\mathrm{i}}+1.5 \hat{\mathrm{j}}+2.5 \hat{\mathrm{k}} \\ \vec{s} &=\overrightarrow{\mathrm{u}} \mathrm{t}+\frac{1}{2} \overrightarrow{\mathrm{a}} \mathrm{t}^{2} \\ &=0+\frac{1}{2}(\hat{\mathrm{i}}+1.5 \hat{\mathrm{j}}+2.5 \hat{\mathrm{k}})(16) \\ &=8 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}+20 \hat{\mathrm{k}} \\ \Rightarrow \mathrm{b} &=12 \end{aligned}

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