Solution:

Initial velocity \(vec{v}_0 = 3\hat{i} + 4\hat{j}\). Acceleration \(\vec{a} = 0.4\hat{i} + 0.3\hat{j}\). Time \(t = 10\text{ s}\). Using \(\vec{v} = \vec{v}_0 + \vec{a}t\), we get \(\vec{v} = (3\hat{i} + 4\hat{j}) + (0.4\hat{i} + 0.3\hat{j})(10) = (3\hat{i} + 4\hat{j}) + (4\hat{i} + 3\hat{j}) = 7\hat{i} + 7\hat{j}\). Speed is the magnitude of velocity: \(|\vec{v}| = \sqrt{7^2 + 7^2} = \sqrt{49+49} = \sqrt{98} = 7\sqrt{2}\).