(II) A driver notices that her 950-kg car, when in neutral, sl...

Question

(II) A driver notices that her 950-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 km/h?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve for this problem on a flat horizontal highway, a 350 kg motorcycle speed drops from 86 kilometers per hour to 70 kilometers per hour in 5.0 seconds. While it is in neutral gear, calculate what the approximate value of power both in watts and horse power that will be needed for the motorcycle to maintain a constant speed of 72 kilometers per hour on the highway. So that's our final answer that we're trying to solve for us. We're trying to figure out what the approximate value of power that is needed for the motorcycle to maintain a constant speed of 72 kilometers per hour on the highway. And we're asked to find our answer in both units of watts and in units of horsepower. Awesome. So looking at our multiple choice answers, all of our first answers are in units of watts and all of our second answers are in units of horsepower. So let's read them off to see what our final answer pair might be. A is 2.1 multiplied by 10 to the power of four and 47. B is 2.1 multiplied by 10 to the power of four and 29 C is 6.7 multiplied by 10 to the power of three and 14. And finally, D is 6.7 multiplied by 10 to the power of three and 9.0. Awesome. So first off, let us note that while the motorcycle's wheels are in neutral gear, they can turn independently from the engine. So in order for the motorcycle to maintain a constant speed or to maintain its constant speed during this particular speed drop, the engine would need to compensate for this power loss by providing the same amount of power. So now let us write down all of our known variables and let's make a quick note here that we need to also convert all of our units of kilometers per hour to meters per second to help keep our units consistent during our solving process, which this will make more sense in a second, but writing down all of our known variables. So we know that our initial velocity of the motorcycle is equal to 86 kilometers per hour and this is equal to 86 kilometers per hour. And we're gonna use dimensional analysis to convert kilometers per hour to meters per second. So let's note that in one, there's 1000 meters in one kilometer. And let us note that in one hour, there is 3600 seconds. So when we plug that into our calculator, we will get 23.889 and its units will be meters per second. And the final velocity of our motorcycle which will be VF will be equal to 70 kilometers per hour, which like our initial velocity, we need to convert 70 kilometers per hour to meters per second. So let's remember that there's 1000 m in one kilometer multiplied by, in one hour, there is 3600 seconds. And once again, we're using dimensional analysis. So when we plug that into our calculator, we will find that our final velocity of the motorcycle and meters per second is 19.444 m per second. And let us note for both the initial velocity and the final velocity, we round it to three decimal places. OK? Let's also note that the mass of the motorcycle, which I'm gonna denote as capital M is equal to 350 kg. And the time taken the slowdown will be equal to t which is equal to 5.0 seconds in this case. So now at this stage, we must recall and use the work energy principle equation which states that the work is equal to the change in kinetic energy delta ke which is equal to one half multiplied by capital M multiplied by VF squared minus one half, multiplied by capital M multiplied by V I squared. So now at this point, we must plug in all of our known variables and solve for the numerical value of W which is the numerical value of work. So the work is equal to one half multiplied by 350 kg multiplied by our final velocity squared. So 19.444 and don't forget your units, which is 19.444 m per second. And this value is squared minus one half multiplied, multiplied by 350 kg multiplied by our initial velocity which is 23.889 m per second. And this is also squared awesome. And when we plug that into our calculator, we will find that it's equal to negative 3000 three hun so sorry, negative 33707 0.66 jules which is the negative 33,707 0.66 jewels. So now we must recall and use the average rate of power loss equation which states that P is equal to the absolute value of W divided by T. So now we need to plug in all of our known variables and solve for P. So when we do that, we will get the absolute value of negative 33707.66 jewels. Don't forget your other absolute value sign all divided by T which is the time, which is 5.0 seconds. So when we plug that into our calculator, when we, we will get in scientific notation, we will get 6.7 multiplied by 10 to the power of three watts when we round to one decimal place. So now we need to convert watts to mechanical horsepowers or HP horsepower for short. So we need to take our answer which I rounded to one decimal place. But initially when you plug it into your calculator, you will get 6.7415 multiplied by 10 to the power of three watts. So let's use this to make sure we get a more precise answer for our horsepower conversion. So we will use 6.7415 multiplied by 10 to the power three watts. So using dimensional analysis, we know that in one horse power there is 746 watts. So when we plug that into our calculator, we will get 9.03686 HP, which is approximately equal to 9.0 HP, which is our final answer in horsepower units. Hooray, we did it. So therefore, we found our final two answers. Fantastic. So looking at our multiple choice answers, the correct answer has to be the letter D which is 6.7 multiplied by 10 to the power of three watts and 9.0 HP. And that's it, we solve for this problem. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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(II) A driver notices that her 950-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 km/h?

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