Three forces F 1 = 10   N ,   F 2 = 8   N ,   F 3 = 6   N are acting on a particle…

When the force $F_1$ is removed, the particle starts accelerating because of the resultant force between $F_2$ and $F_3$.

The resultant force can be calculated as follows:

$\begin{array}{rcl}F& =& \sqrt{{F_2}^2+{F_3}^2}\\ & =& 10 \mathrm{N}\end{array}$

Hence, the acceleration of the particle is given by

$\begin{array}{rcl}a& =& \frac{10 \mathrm{N}}{5 \mathrm{kg}}\\ & =& 2 \mathrm{m} {\mathrm{s}}^{–2}\end{array}$