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A body moves in X - Y plane under the action of acceleration given by $\frac{1}{3}(6t\hat{i} + 4t\hat{j})$. Assuming that the body is at rest at time $t = 0$, the velocity of body at $t = 3\text{sec}$ is
Explanation
$a_{x} = 6t/3$, $a_{y} = 4t/3$ so $u_{x} = \int_{0}^{t}{a_{x}dt} = t^{2} \Rightarrow (u_{x})_{t=3} = 9 m/\text{sec}$ and $u_{y} = \int_{0}^{t}{a_{y}dt} = 2t^{2}/3 \Rightarrow (u_{y})_{t=3} = 6 m/\text{sec}$ (because $u_{x}$ & $u_{y} = 0$ at $t = 0\text{sec}$)