# A car weighing 2000 kg starts to move and goes uphill, the slope of which is 0.02. After covering a distance of 100 m

**A car weighing 2000 kg starts to move and goes uphill, the slope of which is 0.02. After covering a distance of 100 m, it develops a speed of 32.4 km / h. Resistance coefficient 0.05. Determine the average power delivered by the car engine.**

To determine the average engine power of the presented car at 100 meters, we apply the formula: N = F * Vav = (m * a + Ftr + Ft * sinα) * (Vk + 0) / 2 = (m * a + μ * m * g * cosα + m * g * sinα) * Vk / 2 = (Vk ^ 2 / 2S + μ * g * cosα + g * sinα) * m * Vk / 2.

Variables and constants: Vk – the achieved speed (Vk = 32.4 km / h = 9 m / s); S – distance traveled (S = 100 m); μ – coeff. resistance (μ = 0.05); g is the acceleration of gravity (g = 9.81 m / s2); α – slope angle of the hill (with a slope of 0.02 α = 1.146º); m is the mass of the presented car (m = 2000 kg = 2 * 103 kg).

Calculation: N = (Vk2 / 2S + μ * g * cosα + g * sinα) * m * Vk / 2 = (92 / (2 * 100) + 0.05 * 9.81 * cos 1.146º + 9.81 * sin 1.146º) * 2 * 103 * 9/2 = 9.82 * 103 W.

Answer: The average engine power of the presented car is 9.82 kW.