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Referring to Example $2-17$ Suppose the speeder (red car) is traveling with a constant speed of $25 \mathrm{m} / \mathrm{s},$ and the maximum acceleration of the police car (blue car) is 3.8 $\mathrm{m} / \mathrm{s}^{2}$ . If the police car is to start from rest and catch the speeder in 15 s or less, what is the maximum head-start distance the speeder can have? Measure time from the moment the police car starts.

$52.5 \mathrm{~m}$

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

Cornell University

Rutgers, The State University of New Jersey

University of Washington

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04:16

In mathematics, a proof is…

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In mathematics, algebra is…

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A speeder passes a parked …

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see Sample Problem $D$ A c…

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A car traveling 25 $\mathr…

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Okay, so and this problem we have of bullies car, there was stuff, which means with initial velocity zero, we have, uh, another car I speeder with constant velocity off 25 meters per second. What else do you have? We know that the acceleration, the maximum acceleration off the police car is 3.8 meters for second square. We want to know what is the maximum distance this Peter can have from the police car. So the bullet scar is stocked chasing this Peter and catch this pewter under a time off 15 seconds. Okay, so let's go. This Peter object A and the police car object be. We have our equation to describe the moment when the police car catches the this. Peter, we know that this moment, the final position off this Peter is equal the final position off the police car. So we just need to describe the position of this Peter in the position of the police car. The position of dispute er is going to be x eight equals x zero. A less v t axel away is what we want to discover. Because is the distance the maximum distance of this Peter from the police car in the beginning of the movement. Let's see, What is the creation from for the police car? It's going to be x zero b waas V zero t loss a d squared divided by two. So we just need two years This information that the final position of the both ours is the same. Then we're going to have X, you know, a less 25 times 15 eco's initial position. Come back here in the show position off. Ah, well, this car is zero, so initial position is going to be zero initial velocity of the police car is also zero. So this is going to be just three point eight times 15 square divided by true. So the maximum distance off the speeder. So the bullet scar King catcher catcher is going to be, let's see three 0.8 times, 15 scrag divided by two minus 15 times 25. So the answer to this it the answer is just maximum had start. It's going to be 52 point five meters. So this is the answer

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