A) \[18\text{ }\hat{i}+3\hat{j}\]
B) \[18\,\hat{i}+6\hat{j}\]
C) \[3\,\hat{i}+18\hat{j}\]
D) \[18\,\hat{i}+4\hat{j}\]
Correct Answer: B
Solution :
\[\vec{a}=\frac{{\vec{F}}}{m}=2{{t}^{2}}\,\hat{i}+\frac{4}{3}\,t\,\hat{j}\] \[d\,\vec{v}=(2{{t}^{2}}\,\hat{i}+\frac{4}{3}\,t\,\,\hat{j})dt\] Integrate on both sides \[\vec{v}=2\,\left[ \frac{{{t}^{3}}}{3} \right]\,\hat{i}+\frac{4}{3}\,\left[ \frac{{{t}^{2}}}{2} \right]\,\hat{j}\] at \[t=3\,\sec .\] \[\vec{v}=\frac{2}{3}{{(3)}^{3}}\,\hat{i}+\frac{4}{6}\,{{(3)}^{2}}\,\hat{j}=18\,\hat{i}+6\,\hat{j}\]
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