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# Question 3d: 2015 AP Physics 1 free response

More analytically analyzing how doubling spring compression impacts stopping distance.

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## Video transcript

- [Voiceover] All right, part d. Explain how any correct aspects of the student's reasoning identified in part b are expressed by your mathematical relationships in part c, and explain how your relationship in part c correct, how your relationships in part c correct any incorrect aspects of the student's reasoning identified in part b. It's a bit of a mouthful, but they're just saying, "Hey, kinda connect the dots between part c" "and the two parts of part b." Refer to the relationships you wrote in part c, not just the final answer you obtained by manipulating those relationships. And so we can, let me write it down here. So d. So part c shows us that doubling, doubling compression does result in more potential energy. Doubling compression does result in more, in more energy. And you could clarify that this is, this is potential, potential and kinetic at different points in time. And then we could even draw a line to it. So we see that, we see that right over here. That is, that is these, that line, and then that line right over there shows that. So I could draw a bit of an arrow to it. They want us to reference some of what we saw before. And just to make it clear, I can put in parentheses. I can show that U two is equal to four U one, and that K two is equal to four, four K one. However, however, however, since the kinetic energy, since the kinetic energy is four times greater, and you have the same, same force of friction, force of friction, the distance is going to be four times as long. The stopping distance, distance, is going to be four times as much. Is going to be four times as long. And even when we, so the correct parts. Part c shows us that doubling the compression does result in more energy. And I could add and more stopping distance. Let me do it there. And more stopping, stopping distance. Whoops. And more stopping distance. And the stopping distance, that arrow is easier to draw. And more stopping distance. However, since the kinetic energy is four times greater, and you have the same force of friction, the stopping distance is going to be four times as long. And we saw that as well over there. So we're saying hey look, the student was right that more compression is more energy, more stopping distance. However, it's going to be four times as long, the stopping distance, not two times as, not two times as far. And there you go.