(i) (a) The power developed by the engine is given by the formula:

\(P = Fv\)

where \(F = 1550 \text{ N}\) and \(v = 40 \text{ m s}^{-1}\).

\(P = 1550 \times 40 = 62000 \text{ W} = 62 \text{ kW}\).

(b) The new power is \(62 \text{ kW} - 22 \text{ kW} = 40 \text{ kW} = 40000 \text{ W}\).

Let \(DF\) be the new driving force. Then:

\(40000 = DF \times 40\)

\(DF = 1000 \text{ N}\).

Using Newton's second law:

\(DF - 1550 = 1100a\)

\(1000 - 1550 = 1100a\)

\(-550 = 1100a\)

\(a = -0.5 \text{ m s}^{-2}\) or \(d = 0.5 \text{ m s}^{-2}\).

(ii) The driving force \(DF\) is given by:

\(DF = 1100g \sin 8^{\circ} + 1550\)

\(DF = 3081 \text{ N}\).

The power equation is:

\(80000 = 3081v\)

\(v = \frac{80000}{3081} \approx 26 \text{ m s}^{-1}\).