Resistance to the motion of an automobile consists of road friction, which is almost independent of speed, and air drag, which is proportion

Question

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.

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Sigridomena 4 years 2021-08-17T19:51:07+00:00 1 Answers 14 views 0

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  1. Nho
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    2021-08-17T19:52:30+00:00
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    Answer:

    \dot W = 4310.924\,W (5\,hp)

    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:

    \dot W = \frac{d}{dt} (\vec P) \bullet \vec v + \vec P \bullet \frac{d}{dt}(\vec v)

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

    \Sigma F = P - 300-1.8\cdot v^{2} = (1500\,kg)\cdot (0.90\,\frac{m}{s^{2}} )

    P = 1850 + 1.8\cdot v^{2}

    The power required at a given velocity is:

    \dot W = 3.6\cdot v^{2} \cdot a + (1850 + 1.8\cdot v^{2})\cdot a

    \dot W = (1850 + 5.4\cdot v^{2})\cdot a

    The output at v = 84\,\frac{km}{h} is:

    \dot W = [1850 + 5.4\cdot (23.333\,\frac{m}{s})^{2}]\cdot (0.90\,\frac{m}{s^{2}} )

    \dot W = 4310.924\,W (5\,hp)

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