a car with a curb weight of 3875 lb, whose engine is rated at 426 hp, is capable

Question

a car with a curb weight of 3875 lb, whose engine is rated at 426 hp, is capable of accelerating from 0 to 60.0 mph in 47.0 s. A. Assuming the power output of the engine is constant, calculate how much horsepower must appear at the wheels for this to happen.
B. Assuming the power output at the wheels is the same aa in part a, calculate the time for the car to accelerate from 0 to 60.0 mph up a 30.0 degree grade.
a car with a curb weight of 3875 lb, whose engine is rated at 426 hp, is capable of accelerating from 0 to 60.0 mph in 47.0 s. A. Assuming the power output of the engine is constant, calculate how much horsepower must appear at the wheels for this to happen.
B. Assuming the power output at the wheels is the same aa in part a, calculate the time for the car to accelerate from 0 to 60.0 mph up a 30.0 degree grade.
A. Assuming the power output of the engine is constant, calculate how much horsepower must appear at the wheels for this to happen.
B. Assuming the power output at the wheels is the same aa in part a, calculate the time for the car to accelerate from 0 to 60.0 mph up a 30.0 degree grade.

Explanation / Answer

part a:

work done = change in Ke = 1/2 mv^2 = 0.5*1757.67 kg * (96.5606)^2 = 8194213.1345 J

Power = work done/time = 174344.960 Watt

since 1 hp = 746 watt, Power = 174344.960/746 = 233.70638 hp

part b:

with out slope/grade: distace coverted : x = v*t = 96.5606*47 = 4538.3482 m

here, height = 4538.3482*sin(30) = 2269.1741 m

power = 233.706 hp = work/time

work = (1/2)mv^2 + mgh = 8194213.1345 + 1757.67*9.8*2269.1741 = 47281113.6899 J

so, time = work/power = 47281113.6899/174344.960 = 271.1928 sec.

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