(i) To find the acceleration at A, use Newton's second law. The driving force provided by the engine is given by:

\(\text{Driving force} = \frac{20,000}{10} = 2000 \text{ N}\)

Using the equation \(DF - R = ma\), where \(R = 500 \text{ N}\), we have:

\(2000 - 500 = 1200a\)

\(1500 = 1200a\)

\(a = \frac{1500}{1200} = 1.25 \text{ m/s}^2\)

(ii) To find the distance AB, consider the work-energy principle. The change in kinetic energy (KE) is:

\(\Delta KE = \frac{1}{2} \times 1200 \times (25^2 - 10^2) = 315,000 \text{ J}\)

The work done by the car's engine is:

\(\text{Work done} = \frac{20,000 \times 30.5}{1} = 610,000 \text{ J}\)

The work done by the engine is equal to the increase in KE plus the work done against resistance:

\(610,000 = 315,000 + \text{Work done against resistance}\)

\(\text{Work done against resistance} = 610,000 - 315,000 = 295,000 \text{ J}\)

Since \(\text{Work done against resistance} = R \times AB\), we have:

\(500 \times AB = 295,000\)

\(AB = \frac{295,000}{500} = 590 \text{ m}\)