Automobile Engine Input Power

## Question:

A car has a mass of 2300 kg and accelerates from rest at 6 m/s^2. Drag on the car due to air resistance is 10*v N where v is the car velocity in m/s. Determine the power supplied to the car's engine at time t=5 seconds. The engine has a running efficiency of 0.68.

## Answer:

The force required of the engine is that required to accelerate the car at the given rate, and to overcome air resistance. The velocity after 5 seconds of acceleration at 6 m/s^2 is 30 m/s. The force required just to maintian the acceleration of the car is F=m*a = 2300*6 = 13,800 N. To overcome drag at 30 m/s and additional force of 300 N is required. Work is force times distance and power is the rate of doing work so power is force times velocity. The power in this case is 14,100 N * 30 m/s = 423,000 Joules/s = 423kw. In order to develop this power the engine must have 423 kw/0.68 supplied = 622 kw.

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