(i) (a) To find the acceleration of A, use the equation of motion:

\(v = u + at\)

where \(v = 5 \text{ m s}^{-1}\), \(u = 0\), and \(t = 2 \text{ s}\).

Substitute the values:

\(5 = 0 + 2a\)

\(a = \frac{5}{2} = 2.5 \text{ m s}^{-2}\)

(b) To find the tension in the string, apply Newton's second law to particle A:

\(0.5g - T = 0.5 \times 2.5\)

\(T = 0.5g - 0.5 \times 2.5\)

\(T = 0.5 \times 9.8 - 1.25\)

\(T = 4.9 - 1.25 = 3.75 \text{ N}\)

(ii) To find the value of m, apply Newton's second law to particle B:

\(T - mg = 2.5m\)

Substitute \(T = 3.75\) and solve for \(m\):

\(3.75 - mg = 2.5m\)

\(3.75 = mg + 2.5m\)

\(3.75 = m(g + 2.5)\)

\(m = \frac{3.75}{g + 2.5}\)

\(m = \frac{3.75}{9.8 + 2.5}\)

\(m = \frac{3.75}{12.3} \approx 0.3 \text{ kg}\)