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TECHNOLOGY A Lamborghini Aventador accelerates from rest to 100 km / h in 2.9 s. The mass of the car is 1575 kg Calculate the power supplied by the car's engine in HP without considering drag and friction (I HP 745.7 W)

Respuesta :

AL2006

At 100 km/hr, the car's kinetic energy is

KE = (1/2) (mass) (speed)²

KE = (1/2) (1575 kg) ( [100 km/hr] x [1000 m/km] x [1 hr/3600 sec] )²

KE = (787.5 kg) (27.78 m/s)²

KE = 607,639 Joules

In order to deliver this energy in 2.9 seconds, the engine must supply

(607,639 J / 2.9 sec) = 209,531 watts

Power = 281 HP

boffeemadrid

We need to find the power supplied to a car in horsepower.

The power supplied to the car's engine is 281.06 HP.

v = Velocity of car = 100 km/h

t = Time taken = 2.9 s

m = Mass of car = 1575 kg

Converting velocity of to m/s

[tex]100\times \dfrac{1000}{3600}=\dfrac{1000}{36}\ \text{m/s}[/tex]

Energy is given by

[tex]E=\dfrac{1}{2}mv^2\\\Rightarrow E=\dfrac{1}{2}\times 1575 \left(\dfrac{1000}{36}\right)^2\\\Rightarrow E=\dfrac{5468750}{9}\ \text{J}[/tex]

Power is given by

[tex]P=\dfrac{E}{t}\\\Rightarrow P=\dfrac{\dfrac{5468750}{9}}{2.9}\\\Rightarrow P=\dfrac{54687500}{261}\ \text{W}[/tex]

Converting to HP

[tex]1\ \text{HP}=745.7\ \text{W}[/tex]

[tex]1\ \text{W}=\dfrac{1}{745.7}\ \text{HP}[/tex]

[tex]\dfrac{54687500}{261}\ \text{W}=\dfrac{54687500}{261}\times \dfrac{1}{745.5}=281.06\ \text{HP}[/tex]

The power supplied to the car's engine is 281.06 HP.

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