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The car starts from rest at $s=0$ and increases its speed at $a_{l}=4 \mathrm{m} / \mathrm{s}^{2}$. Determine the time when the magnitude of acceleration becomes $20 \mathrm{m} / \mathrm{s}^{2}$. At what position $s$ does this occur?

$t=7$ seconds $d=98 \mathrm{m}$

02:34

Zulfiqar A.

Physics 101 Mechanics

Chapter 12

Kinematics of a Particle

Motion Along a Straight Line

Newton's Laws of Motion

Applying Newton's Laws

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in this question. We have a car moving along a circular art. Yeah. And then, uh, three years off curvature is for the meters and then is traveling along this art and s from rest. Okay, so the the length of the, uh, the hard thing of the Yeah, trajectory is s mhm. So, um, you are given that the tangential acceleration is formulas for the second square. So the cost is suffering. Rest with this acceleration until the acceleration becomes 20 m per second squared is the total acceleration We want to find the time. And the physician Uh huh. When that occurs. Okay. So, um, so since the car, uh, it's moving in a circular track. Okay. Yes, uh, the normal component in the acceleration and attending to a component of the acceleration. Okay, The normal component is, uh, the square over wrong. Okay, this is wrong. We s r 80 times t because there's no initial speed, so it's just 80 times t and then there are viral. And then if you substitute 80 you get 16 divided by for the key square. Okay, 0.4 key square. Okay, then, uh, given that mm, He is 20 m per second square, and this is equal to a N square plants. 80 square square roots. Okay, so, uh, okay. Fly red equals two A and 0.4 square and a square. It plus four square. So you have 0.16 You do the fall if you go to 419 16, which is 384 s. O. T s. It looks like this. And you got, um, 6.99 seconds, which is, um, 7 2000 seconds. Okay. Mhm. So we can find a B. Yeah, this time will be 80 times. He four times seven. You get 28.0 m per second. Okay, so this is one of the answer, and then you use, um, we square. It goes to the North Square, plus to a t s. Okay. And we can have, uh, we have Rina equals 0. 80 equals four. And then B s 28. Yes. Second. And so we have Delta s. It goes to the square over to 18. 28 squared, divided by two times four. When you get 98.0 m. Cool. And that's all for this question.

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