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A battery-operated car utilizes a 12.0 V system. Find the charge the batteries must be able to move in order to accelerate the 750 kg car from rest to 25.0 m/s, make it climb a $2.00 \times 10^{2} \mathrm{m}$ high hill, and then cause it to travel at a constant 25.0 $\mathrm{m} / \mathrm{s}$ by exerting a $5.00 \times 10^{2} \mathrm{N}$ force for an hour.

$q=3.89 \times 10^{6} \mathrm{C}$

Physics 102 Electricity and Magnetism

Chapter 19

Electric Potential and Electric Field

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Cornell University

Simon Fraser University

Hope College

University of Sheffield

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all right. So in this problem we have a car model whose mess is Ah, 77 50 kilograms. And we also know that Ah, initially the car is that arrest. So there's a car Initially it is that arrest and that is accelerated. Thio velocity 25 meters per second initially zero and then the clams up with the hide off 200 meters and then it's just go on with the constant velocity. But there is ah, resistance. The resistance is ah ah 200 Newton's so, uh suppose the voltage of the batteries of equal 12 waltz. So I want to find out to the total chart that that this battery moved. So first we need to find out the total energy of the system that did the car used be equal. Initially, it is the velocity transfer from 0 to 25 right? So ah, the kind of energy is half and times V's quit and then stay dirty. That ah applied thio move this car from the bottom to the top to the to the top. So it's a plus on G H. And they it's the energy used it to overcome the resistance plus f times v. Times t. Right? So Ty's one hour and your plan will you just plugging all the values into this expression and you will see that the two energy is, ah, six point 4.67 times 10 to the seven jos and this energy also equal thio v Times Q Bear Visa about eight over here and accuse the char that that this better transfers So you can plug in the video of the 12th into this expression, and you contend that the Q equal 3.89 times turned to the six corpse.

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