A 1235.2 kg car climbs a 9.4° slope at a constant speed of 94.4 km/h. Assuming that air resistance may be neglected, at what rate (in kW) must the engine deliver energy to the drive wheels of the car

Power is equal to work over time, and work is equal to force times distance. Thus we can show that power is equal to force times velocity. By drawing a free body diagram and applying Newton's second law of motion, we can find the required force to move the car up the slope.

There are 3 forces on the car:

Weight force mg pulling down,

Normal force N pushing up perpendicular to the slope,

and applied force F pushing up parallel to the slope.

Sum of forces in the parallel direction:

∑F = ma

F − mg sin θ = 0

F = mg sin θ

F = (1235.2 kg) (9.8 m/s²) (sin 9.4°)

F = 1977 N

The speed of the car is 94.4 km/h. Converting to m/s:

v = 94.4 km/h × (1000 m/km) × (1 h / 3600 s)

v = 26.22 m/s

So the power is:

P = Fv

P = (1977 N) (26.22 m/s)

P = 51,843 W

P = 51.8 kW