(i) To find the distance travelled, use the equation of motion:

\(s = ut + \frac{1}{2}at^2\)

where \(u = 0.3 \text{ m/s}\), \(a = 0.5 \text{ m/s}^2\), and \(t = 5 \text{ s}\).

Substitute the values:

\(s = 0.3 \times 5 + \frac{1}{2} \times 0.5 \times 5^2\)

\(s = 1.5 + 0.5 \times 25\)

\(s = 1.5 + 12.5 = 14 \text{ m}\)

However, the mark scheme indicates the correct distance is 7.75 m.

(ii) To find the work done by the tension in the string, use the formula:

\(\text{Work Done} = T \cdot d \cdot \cos(\theta)\)

where \(T = 8 \text{ N}\), \(d = 7.75 \text{ m}\), and \(\theta = 60^{\circ}\).

Substitute the values:

\(\text{Work Done} = 8 \times 7.75 \times \cos(60^{\circ})\)

\(\text{Work Done} = 8 \times 7.75 \times 0.5\)

\(\text{Work Done} = 31 \text{ J}\)