A drone is initially at rest at the origin of an \(xy\)-coordinate system. At time \(t=0\), the drone's engines are engaged, giving it an acceleration vector \(\vec{a}(t)\) as a function of time \(t\) given by the equation:
\[ \vec{a}(t) = (\alpha t) \hat{i} + (\beta - \gamma t) \hat{j} \]
where \(\alpha = 1.2 \text{ m/s}^3\), \(\beta = 4.0 \text{ m/s}^2\), and \(\gamma = 0.6 \text{ m/s}^3\).