(i) Apply Newton's second law to particle P:

\(0.6g - T = 0.6a\)

Apply Newton's second law to particle Q:

\(T - 0.2g = 0.2a\)

Add the two equations:

\(0.6g - T + T - 0.2g = 0.6a + 0.2a\)

\(0.4g = 0.8a\)

Solve for acceleration \(a\):

\(a = \frac{0.4g}{0.8} = 5 \text{ m/s}^2\)

Substitute \(a = 5\) into the equation for P:

\(0.6g - T = 0.6 \times 5\)

\(T = 0.6g - 3\)

\(T = 3 \text{ N}\)

(ii) Use the equation of motion \(s = ut + \frac{1}{2}at^2\) with \(s = 0.9\), \(u = 0\), \(a = 5\):

\(0.9 = \frac{1}{2} \times 5 \times t^2\)

\(t^2 = \frac{0.9 \times 2}{5}\)

\(t^2 = 0.36\)

\(t = 0.6 \text{ s}\)