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(I) One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by $7.0 \mathrm { m } / \mathrm { s } ,$ they then have the same kinetic energy. What were the original speeds of the two cars?

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$v_{1}=4.95 \mathrm{~m} / \mathrm{s}$ $\\$$v_{2}=9.90 \mathrm{~m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

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So here we first need to know that the mass of one is equal to two times the mass of two. Ah, given this, we know that the initial kinetic energy of the first mass is equal to half of the initial kinetic energy of the second mass. We also know that 1/2 times mass someone visa one squared equals one 1/4 brother I'm Cem to Visa two squared. So if we have this, we can say that we can also create another relationship and say that the final kinetic energy equals the the final candidate. Energy of the first mass equals the final kinetic energy of the second mass and then substituting for this we have 1/2 times amps of one time's beasts of one plus seven meters per second squared equals 1/2 and some to be septuplets. Seven squared. So at this point, we can substitute in for this and say that one over two times two times mass sub, too. Time's velocities of one squared would be equal to one over four mass of two velocities of two squared The mass, of course, cancels out on DH. We have that two times the velocity of the first mask equals the velocity of the second mask. Second mass mask. My apologies, this mess. And then let's substitute this relationship in for this equation here and say that 1/2. Rather, let's get a new workbook 1/2 times. I'm so 1/2 times two amps up, too. Time's Visa one plus seven squared equals 1/2 times M sub, too. Time's Visa two plus seven squared. And so we can say that two times V's of one plus seven squared equals Visa two plus seven squared. Given that all of this cancels out and so we can say, Well, that that this cancels out And so we can say that if we were to solve for this, we can say that, um, two times Visa of one plus seven squared equals two times the size of one plus seven squared and then solving for visa of one, it's something going to be 4.95 meters per second, and then we know that V sub two is equaling two times piece of one. So visa, too, is simply equal to 9.90 meters per second. So these air beer to final answers. That is the end of the solution. Thank you for watching

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