To solve this problem, let's calculate the net force applied to the particle and then use Newton's second law ($F = ma$) to determine the acceleration.

Step 1: Calculate the net force

The two forces are given as: $\mathbf{F}_1 = 5.0 \, \mathbf{\hat{i}} + 7.0 \, \mathbf{\hat{j}} \, \text{N}$ $\mathbf{F}_2 = -3.0 \, \mathbf{\hat{i}} + 8.0 \, \mathbf{\hat{j}} \, \text{N}$

The net force is: $\mathbf{F}_{\text{net}} = \mathbf{F}_1 + \mathbf{F}_2$ [ \mathbf{F}_{\text{net}} = (5.0 - 3.0) , \mathbf{\hat{i}} + (7