A body of mass 2 kg moves under a force of $\left( {2\widehat i + 3\widehat j + 5\widehat k} \right)$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)

$\overrightarrow F = (2\widehat i + 3\widehat j + 5\widehat k)N$<br><br>time = 4 sec<br><br>As body start from rest therefore <br>position vector initially $\overrightarrow {{r_i}} = (0\widehat i + 0\widehat j + 0\widehat k)$ &amp; <br>u (initial velocity) = 0<br><br>given, ${r_f} = (x\widehat i + y\widehat j + z\widehat k)$<br><br>Now, from second equation of motion<br><br>$\overrightarrow s = \overrightarrow u t + {1 \over 2}\overrightarrow a {t^2}$<br><br>$${r_f} - {r_i} = {1 \over 2} \times \left( {{{2\widehat i + 3\widehat j + 5\widehat k} \over 2}} \right) \times {(4)^2}$$<br><br>$\Rightarrow$ $$(x\widehat i + y\widehat j + z\widehat k) - (0\widehat i + 0\widehat j + 0\widehat k) = 8\widehat i + 12\widehat j + 20\widehat k$$<br><br>$\Rightarrow$ $$x\widehat i + y\widehat j + z\widehat k = 8\widehat i + 12\widehat j + 20\widehat k$$<br><br>$\therefore$ The value of b = 12