Final answer:
The average power of the engine needed for a 2000 kg car to accelerate from 0 to 30 m/s in 6s is 150 kW, which was found using the work-energy principle and the definition of power.
Step-by-step explanation:
To calculate the average power of the engine needed for a 2000 kg experimental car to accelerate from 0 to 30 m/s in 6s, we will use the work-energy principle and the definition of power.
First, we find the kinetic energy (KE) at 30 m/s using the formula KE = (1/2)mv2, where m is mass and v is velocity.
KE = (1/2) × 2000 kg × (30 m/s)2 = 900,000 J (joules)
Power is defined as work done per unit time. The work done on the car is equal to the change in kinetic energy, which is 900,000 J over a time of 6 seconds:
Average Power = Work done / Time = 900,000 J / 6 s = 150,000 W
Converting watts to kilowatts, we get 150,000 W = 150 kW, which isn't listed in the options provided. However, there could have been a typographical error or misunderstanding in the options. The closest correct answer from the options provided would be (c) 25 kW but this is actually incorrect based on the calculations.