To find the force produced by the engine, we use the formula for power:

\(P = F \times v\)

where \(P = 8000 \text{ W}\) (since 8 kW = 8000 W) and \(v = 25 \text{ m/s}\). Solving for \(F\):

\(F = \frac{P}{v} = \frac{8000}{25} = 320 \text{ N}\)

To find the resistance to motion, we apply Newton's second law:

\(F - R = ma\)

where \(F = 320 \text{ N}\), \(m = 100 \text{ kg}\), and \(a = 0.5 \text{ m/s}^2\). Solving for \(R\):

\(320 - R = 100 \times 0.5\)

\(320 - R = 50\)

\(R = 320 - 50 = 270 \text{ N}\)