An object of mass 3 kg is at rest. Now a force of $\overrightarrow{F}=6t^2\hat{i}+4t\hat{j}$  is applied on the object then velocity of object at $t=3 \sec$ is

$$\begin{gathered} \overrightarrow{F}=6t^2\widehat{i}+4t\hat{j}; \\ \Rightarrow m\overrightarrow{a}=6t^2\widehat{i}+4t\hat{j}; \\ \Rightarrow \overrightarrow{a}=\frac{6}{3}{t}^2\widehat{i}+\frac{4}{3}t\hat{j} \end{gathered}$$

Integrate from t=0 to t=3 sec to find velocity

$\overrightarrow{\mathrm{v}}={\left(2\left[\frac{{\mathrm{t}}^3}{3}\right]\hat{\mathrm{i}}+\frac{4}{3}\left[\frac{{\mathrm{t}}^2}{2}\right]\hat{\mathrm{j}}\right)}_0^3$

$\overrightarrow{\mathrm{v}}=\frac{2}{3}(3{)}^3\hat{\mathrm{i}}+\frac{4}{6}(3{)}^2\hat{\mathrm{j}}=18\hat{\mathrm{i}}+6\hat{\mathrm{j}}$