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Problem 69

Acceleration The maker of an automobile advertises that it takes 13 seconds to accelerate from 25 kilometers per hour to 80 kilometers per hour. Assume the acceleration is constant.

(a) Find the acceleration in meters per second per seconds.

(b) Find the distance the car travels during the 13 seconds.

Answer

$$

\begin{array}{l}{\text { a) } 1.175 \mathrm{m} / \mathrm{s}^{2}} \\ {\text { b) } 189.583 \text { meters }}\end{array}

$$

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## Discussion

## Video Transcript

catching? 13 seconds. 25 Thio Flummery for Allah. Question is yes. Acceleration in miles per second of our meter per second. So I'm gonna find my zero. I have to change that two meter per second. I have tried. I home one a then leader and 3600 second. So that will change it to meters per second. 25. I get 2 50 over 36 and a meters. One second. I do the same thing at 13. 80 and whom? 36 you for a second. Now they say acceleration is a constant. You want my velocity? You gonna take the integral because it goes position velocity acceleration. There we go back one that go back when I take the int'l growth. So that team and we can substitute the subsea month. It's Hey, we would have these 13. Mmm. Solving these absurd. Oh my what? These 13 he falls. I'm gonna have 800. Oh, you're a six. You won't. I mean a over 36 solving for a I get 800 minus 2 50 because they're coming later home over 36 06 time miles. I subtracted this from dividing by 13 Zane's multiplying by 13 and then a equals about 1.175 and that would be in meters per seconds. And then for part B, we're gonna take our Richie 2 50 group six. And I'm going in to take the integral that to get my ex King because I want to find my position function into grow me lungs a squared plus two only 36 he plus and I really have to do my plus C because the distance equals zero when time soc thanks. And now I'm gonna plug in my 13 seconds for my time and for my acceleration. I'm gonna love you in my one point once, but yeah, and when I do that, I get about 1 89 Bye Boat five mine and that's in meters

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