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$P_{avg}=6.6 \times 10^4 W$

Giancoli 6th Edition, Chapter 6, Problem 60


Chapter 6, Problem 60 is solved.

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Transcript for this Giancoli solution

Knowing that power is force times velocity, average velocity, we'll solve for 'f ' and 'v' and then figure out what the power is, based on that. So we'll start by the saying the force, assuming there's no friction, the force provided by the engine is the only force. So it will be the net force. So that equals ma that is mass times the change in velocity over time. This change in velocity over time is the acceleration. And then we'll say that the average velocity is going to be the initial plus the final velocity, divided by 2. That's true when you have a constant acceleration. And there is no initial velocity cause it starts from there. So that's just 'vf 'over 2. So we'll make substitutions for this and this, and here. We'll actually write this one slightly differently. We'll write mass times final minus initial, divided by 'g'. That final minus initial is the change of velocity. Again being that there's no initial velocity we could actually write that as, mass times final velocity divided by 't'. So we're going to multiply this and this, because that's going to be 'f' times 'v', and that is 'p'. So the power is 'f ' times 'v', 'f' being 'mvf' over 't', times the speed, average speed, which is 'vf 'over 2. So this is mvf squared over 2't'. That's the power output of the car. And we'll substitute in numbers. So we get 'p' is 1400 Kilograms, times a speed of 95 Kilometers per hour, which will change into Meters per second, by dividing by 3.6, square that, divide it by 2 and times 7.4 seconds. This gives us an answer of 6.6 times 10 to the 4 watts. Which is approximately, 88 Horse powers, so we know that this is a reasonable number. 88 Horse power is when you listen to advertisements for cars, it's a plausible Horse power, for a small car.