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Integrated ConceptsA light-rail commuter train draws 630 A of 650-V DC electricity when accelerating. (a) What is its powerconsumption rate in kilowatts? (b) How long does it take to reach 20.0 m/s starting from rest if its loaded mass is $5.30 \times 10^{4} \mathrm{kg},$ assuming 95.0$\%$ efficiency and constant power? (c) Find its average acceleration. (d) Discuss how the acceleration you found for the light-rail train compares to what might be typical for an automobile.

(a) $P=410 \mathrm{kW}$(b) $\Delta t=27.2 \mathrm{s}$(c) $a=0.734 \mathrm{m} / \mathrm{s}^{2}$(d) The acceleration of a typical automobile is greater than the acceleration of a light-rail train.

Physics 102 Electricity and Magnetism

Chapter 20

Electric Current, Resistance, and Ohm's Law

Current, Resistance, and Electromotive Force

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

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up of the given did on that stick given good and I, as 6 30 amperes and even boarded, has given us 6 50 walls, which is an a C word. Now we need to call for the power consumption read. So let's start with step, eh? So write it as power consumption, which is our big generation as Bian Mitch is a combination off I envy. So let's put the values as 6 30 amperes multiplied by 6 50 world. We calculate this and we get the reserved as it's full black, 9500 wards and that its been awarded indicate award certainly before 9.5. Kid once. So basically the answer would be That's right. It down. Power consumption is a quote to approximately 410 kilowatts. And this is on sir for Skippy. No, it started the stem be in order to calculate the time it takes to reach 20 meters per second with the mass off 5.3 into generous to four kilograms. So ask for the given data. This initial velocity is zero made up a second. Let's write down the final velocity Israel, which is training me to per second mass is giving us 5.3 into terrorists to four kilograms and missed. Let's start with the work energy, Tatum. So let us take work and invited him now in this particular cheered him. The work is equal to changing Canada energy. So we need to put it in himself. Questions So work is general s W change in kinetic energy. So it would be half and final velocities square minus half into em into initial velocity square. So I just take the common barometers. You'd be half into em and Brackett will write it as final velocity squared minus initial velocity square. No sins. Initial velocity is you don't make up a second. So therefore we get w us have multiplied by am That is Moss monkey, played by Final Velocity Square. No says it's considered output. Power that is beyond is equal to work done divided by time. So which is generated as w appointee. Therefore, it only took a great time. What is that? A show off road done and I'll put power. So let's put w as half and and every of screw upon our power. So find the need. We get the question for time as he's equal to Mars, we have square upon two times are over. And let us consider this as a question one now, since efficiency is given. So all right, it down. Efficiency is equal to 95% which is always a ratio off our good power of mine into power. So therefore, if I consider be out the result for power, which is 95% to that off input, So write it as 0.95 times being now, this is a question that we need to remember now. Now let's put this while new off, be out in a question. One. So what we're doing here. Therefore, he's equal to I just write down all the bodies now. So it is 5.3 into Dennis to four kg, which is a value of Mars multiplied by final velocity. That is 20 meters per second square, and it is two times PR, so two times being so that is, it's not just being but 0.95 being because the value of B out so that's what the bodies again. So it will be 5.3 into Dennis. You're four kilogram multiplied by 20 meters per second. So that is gonna be 400 and two times 0.95 might applied by four or 9.5 rewards. Now, when we saw this, we're getting the value off time as 27.25 second. And this is the second answer that we have got. So what we can mention here at the time therefore we can write it down. The time taken for the real to acquire the given speed is 27 point to five seconds. It's consider the party to find the average acceleration for the commuter tree. So what we're going to use is kind of magic equation. So which is we? If that is, final velocity is equal to initial velocity, plus multiplication off a celebration and time. This is the kind of medical question that we're going to use not here, but, um ation. It's not just me, but it is a r. So because it is gonna be the real acceleration, so says initial velocity is, you know, meter per second. Therefore, we conventionally if is equal to e. R. Multiplied by D. So therefore, in order to calculate the incineration off computer really is. It's a combination of the F with respect to time. Not while you're free of that. Its final velocity is training me to per second. Time is straight 7.25 seconds. So argument today we get an answer. As you know, born 734 meter bruise, second square. This is 1/3 answer, which we have God so we can even write. Therefore, the average a celebration off the rail is Cedo born 734 meter per second scratch. Let's take barked D the average acceleration off an automobile. So now let's consider the I'll write it down average a celebration off and Entre Mobile is. We'll take the notation that is we f minus. We are a point. It is one of the kinda magic equations that we're using, the same one that we have already used in Step See. So now let's put Rieff and here we can write a movie. If, as 80 kilometer put over, just given value be I that his initial velocity zero kilometer part over and he's given us 10 seconds now solving this rather we get acceleration off. Automobile is equal to a T minus zero upon 10 on. We need answering. Made up a second square. Sorry. Just multiplied by 1000 meters. We're converting kilometers to major and we're converting number of ours in two seconds. So, Mikey Bloodbath 16 to succeed. That is 3600 seconds. So are you meeting Greg getting answer as to point to do media per second square? Now that is compare compared the acceleration off rail with typical acceleration off automobile. So what we're going to do, we're going to decoration. So acceleration of water mobile with this picture rail is equal to let's put the values you don't born 734 meters per second scrap in disarray. Sure, he's coming at st So what we can right here that automobile acceleration But the respect too acceleration off real commuter. Now let's put this in words here toward taking the ride. His hands acceleration Okay, off an automobile is nearly three times the acceleration off brain commuter on this should be our find. An answer

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