A high-precision surgical micro-robot of mass $m$ grams is being navigated through a fluid medium under the influence of two primary forces, $\mathbf{P}$ and $\mathbf{Q}$.

The forces are defined as follows:

$$\mathbf{P}=(0.7\mathbf{i}-3.2\mathbf{j})N$$ $$\mathbf{Q}=(k\mathbf{i}+0.5k\mathbf{j})N$$

where $k$ is a constant scalar.

The resulting acceleration of the micro-robot is measured to be $(2.4\mathbf{i}+0.8\mathbf{j}){m\; s}^{-2}$.

Determine the value of $k$.