A body of mass $2 \mathrm{~kg}$ moves under a force of $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}) \mathrm{N}$. It starts from rest and was at the origin initially. After $4 \mathrm{~s}$, its new coordinates are $(8, b, 20)$. The value of $b$ is______ (Round off to the Nearest Integer)
(12)
$\overrightarrow{\mathrm{a}}=\frac{\overrightarrow{\mathrm{F}}}{\mathrm{m}}=\frac{2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{2}$
$=\hat{\mathrm{i}}+1.5 \hat{\mathrm{j}}+2.5 \hat{\mathrm{k}}$
$\vec{\tau}=\overrightarrow{\mathrm{u}} \mathrm{t}+\frac{1}{2} \overrightarrow{\mathrm{a}} \mathrm{t}^{2}$
$=0+\frac{1}{2}(\hat{\mathrm{i}}+1.5 \hat{\mathrm{j}}+2.5 \hat{\mathrm{k}})(16)$
$=8 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}+20 \hat{\mathrm{k}}$
$\mathrm{b}=12$
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