b
\(\frac{d \vec {v}}{d t}=\vec {a}=\frac{\vec {F}}{m}=\frac{6 t^{2} \hat{i}+4 t \hat{j}}{3} m / s^{2}\)

as acceleration depending on time so its not a

case of constant acceleration hence \(\overrightarrow{v}=\int_{0}^{i} \vec{a} \mathrm{d} t\)

\(\therefore \quad \overrightarrow{\mathrm{v}}=\int_{0}^{3}\left(\frac{6 \mathrm{t}^{2}}{3} \hat{\mathrm{i}}+\frac{4 \mathrm{t}}{3} \hat{\mathrm{j}}\right) \mathrm{dt}\)

\(=\left[\frac{6 t^{3}}{9} \hat{i}+\frac{4 t^{2}}{6} \hat{j}\right]_{0}^{3}=18 \hat{i}+16 \hat{j}\)