First, use the equation of motion to find the acceleration:

\(s = \frac{1}{2} a t^2\)

\(2.25 = \frac{1}{2} a (1.5^2)\)

\(a = 2 \text{ m/s}^2\)

Next, calculate the normal reaction force \(R\):

\(R = mg \cos 30^{\circ}\)

Apply Newton's second law along the plane:

\(mg \sin 30^{\circ} - \mu mg \cos 30^{\circ} = ma\)

\(mg \sin 30^{\circ} - \mu mg \cos 30^{\circ} = 2m\)

Solving for \(\mu\):

\(\mu = \frac{mg \sin 30^{\circ} - 2m}{mg \cos 30^{\circ}}\)

\(\mu = \frac{g \sin 30^{\circ} - 2}{g \cos 30^{\circ}}\)

Substitute \(g = 9.8 \text{ m/s}^2\):

\(\mu = \frac{9.8 \times 0.5 - 2}{9.8 \times \frac{\sqrt{3}}{2}}\)

\(\mu = 0.346\)