Answer :
Answer:
51.8 kW
Explanation:
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
