Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 118

Resistance to the motion of an automobile consists of road friction, which is almost independent of speed, and air drag, which is proportional to speed-squared. For a certain car with a weight of \( 12\,000 \text{ N} \), the total resistant force \( F \) is given by \( F = 300 + 1.8v^2 \), with \( F \) in newtons and \( v \) in meters per second. Calculate the power (in horsepower) required to accelerate the car at \( 0.92 \text{ m/s}^2 \) when the speed is \( 80 \text{ km/h} \).