(i) The driving force when the car is at its greatest speed is given by the resistive force: \(35 \times 60\). The power is then \(35 \times 60^2 = 126000 \text{ W}\).

(ii) The driving force \(\text{DF}\) is \(\frac{126000}{30}\). Using Newton's second law: \(\text{DF} - 35 \times 30 = 1200a\). Solving for \(a\), we have \(a = \frac{3150}{1200} = \frac{21}{8} = 2.625 \text{ m s}^{-2}\).

(iii) The driving force \(\text{DF} = \frac{126000}{v}\). The equation for forces is \(\frac{126000}{v} = 35v + 1200g \times \frac{7}{48}\). Simplifying gives \(35v^2 + 1750v - 126000 = 0\) or \(v^2 + 50v - 3600 = 0\). Solving this quadratic equation gives \(v = 40 \text{ m s}^{-1}\).