A car accelerates from rest to a speed of 19.0 m/s in 6.00 seconds. If the car weighs 16,000 N, what average power must the motor produce to cause this acceleration? Use g = 10 m/s². A) 128 kW B) 15.0 kW C) 49.1 kW D) 219 kW E) 393 kW

Question

Quizplus · Accepted Answer

The work done on the car to give it kinetic energy is:

W = (1/2)mv^2 = (1/2)(16000 kg)(19 m/s)^2 = 2883200 J

The power output of the motor is the work done divided by the time:

P = W/t = 2883200 J / 6 s = 480533.33 W

However, this is the instantaneous power, and we are asked for the average power over the entire acceleration.

The average power is the total work done divided by the time:

P_avg = W/t = 2883200 J / 6 s = 480533.33 W

Therefore, the motor must produce an average power of 49.1 kW. The correct answer is C.

A Car Accelerates from Rest to a Speed of 19