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A car is traveling at $20.0 \mathrm{m} / \mathrm{s},$ and the driver sees a traffic light turn red. After 0.530 s (the reaction time), the driver applies the brakes, and the car decelerates at 7.00 $\mathrm{m} / \mathrm{s}^{2} .$ What is the stopping distance of the car, as measured from the point where the driver first sees the red light?

39.2$m$

Physics 101 Mechanics

Chapter 2

Kinematics in One Dimension

Motion Along a Straight Line

Hope College

University of Winnipeg

McMaster University

Lectures

04:34

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okay were given a car with an initial velocity of 20 meters per second. The driver of the car sees a red light up ahead. It takes the person 0.530 seconds to slow the to hit the brakes, which is called the reaction Time. So we're asked to find how far the car travels while it's stopping. If the acceleration wants the person's foot hits the brakes is negative. Seven leaders per second squared. So we need to break this problem up into two parts. The total displacement is going to be the time. I'm sorry. The total displacement is going to be the displacement traveled while the person is reacting, plus the displacement while the person is breaking. So let's solve for each of those two parts, one at a time, the reaction, displacement a reaction distance. We're just living in one direction so we don't have to brave up direction is just gonna be the velocity that the cars travelling times the time interval that we're discussing, which would be the 10.530 seconds So 20 meters per second times 0.530 seconds. Princesses would give us a distance of 10.6 years. Okay, so that's what the car have. Far. The car moves even before the driver hits the bricks. Okay, well, once the driver hits the brakes, we have we know that the velocity at the end of the problem would be zero meters per second because the cars coming to arrest. So the initial velocity again is 20. Because that's how fast the car is moving before the brakes air hits. The acceleration is negative. Seven. So we're not given the time that it takes for this car to stop, we could find it. But we can also use the equation. The final squared is equal to the initial velocity of the not squared plus two times acceleration times the displacement. So zero equals 20 squared, plus two times negative seven meters per second squared times that displacement. So moving my 20 square to the left hand side, I have negative 400 meter square per second square is equal to negative 14 meters per second squared times X. I need to divide both sides by negative 14 and we have our answer for the breaking distance. Part of this problem, which would be 28.57 x is over here, so 28.57 meters. So we have the two. This is the breaking distance. So the to distances that we need to add together are the 10.6 meters and the 28.7. So my total over here 10.6 meters plus 28 0.57 meters and that's gonna equal 39.2 0.17 meters which rounded to three significant figures, gives us 39.2 and that's our total displacement.

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