Question

A 1,720 kg car accelerates from rest to 22 m/s in 12 seconds. in the process, work by air drag on the car is -40 kj. if the car’s engine/drivetrain is 20% efficient, how much total power must the car engine produce to do this?

Answer 1

The total power the car's engine must produce to accelerate is 16,667 W.Total power = 16,667 W

Step-by-step explanation:

To find the total power that the car's engine must produce, we need to calculate the net work done on the car and apply the efficiency of the car's engine and drivetrain. First, we calculate the net work done using the work-energy theorem:

Net work = change in kinetic energy

Since the car starts from rest, the initial kinetic energy is 0. The final kinetic energy can be found using the equation:
Final kinetic energy = (1/2)mv^2

Plugging in the given values, we have:
Final kinetic energy = (1/2)(1720 kg)(22 m/s)^2 = 417,680 J

The net work done on the car is equal to the negative of the work done by the air drag:
Net work = -40 kJ = -40,000 J

Now, we can calculate the total work done by the car's engine and drivetrain:
Total work = Net work / Efficiency

Substituting the values, we get:
Total work = -40,000 J / 0.20 = -200,000 J

Finally, we can find the total power required by the car's engine:
Total power = Total work / Time

Given that the time is 12 seconds, we can calculate:
Total power = -200,000 J / 12 s = -16,667 W

Since power cannot be negative, we take the absolute value to get the total power required by the car's engine:
Total power = 16,667 W