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 12000 N, the total resistant force F is given by F = 300 + 1.8v2, with F in newtons and v in meters per second. Calculate the power (in horsepower) required to accelerate the car at 0.90 m/s2 when the speed is 84 km/h.

Explanation:

Let assume that vehicle is moving on a horizontal surface and the vehicle mass is 1500 kg. The equation for the power needed to accelerate the car is:

The equivalent engine force needed to accelerate the car is derived from the following equation of equilibrium:

The power required at a given velocity is:

The output at is:

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