A 975-kg sports car accelerates from rest to 95 km/h in 6.4 s. What is the average power delivered by the engine?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The average power delivered by the sports car's engine equals the force delivered by the engine times the speed of the car. So the force is gonna be mass times acceleration and the acceleration is gonna be change in velocity divided by time. And we are given a final velocity and that's gonna be 95 kilometers an hour minus initial velocity of 0 because it's at rest and so this force formula becomes m v f over t. This v, right here, is average velocity so it's v initial plus v final divided by 2; initial again being 0 so this average velocity is v final over 2. And so we substitute for each of those in our power formula; we substitute for force, m v f over t; and we substitute for average velocity, final velocity divided by 2. And then combine these two terms, you get m v f squared over 2 times t and then we plug in numbers. So we have 975 kilograms— mass of the sports car— times 95 kilometers per hour, divide by 3.6 to turn that into meters per second and square that result; and then divide by 2 times 6.4 seconds and you get 5.3 times 10 to the 4 watts or 71 horsepower.