Solution:

Given:

- Initial velocity: \(\mathbf{u} = 3\hat{i} + 4\hat{j}\)
- Acceleration: \(\mathbf{a} = 0.4\hat{i} + 0.3\hat{j}\)

Calculate final velocity after 10 s:

\[
\mathbf{v} = \mathbf{u} + \mathbf{a}t = (3\hat{i} + 4\hat{j}) + (0.4\hat{i} + 0.3\hat{j}) \cdot 10
\]

\[
\mathbf{v} = 3\hat{i} + 4\hat{j} + (4\hat{i} + 3\hat{j}) = (3 + 4)\hat{i} + (4 + 3)\hat{j} = 7\hat{i} + 7\hat{j}
\]

Calculate speed:

\[
\text{Speed} = |\mathbf{v}| = \sqrt{(7)^2 + (7)^2} = \sqrt{49 + 49} = \sqrt{98} = 7\sqrt{2} \, \text{m/s}
\]