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A person driving her car at 45 $\mathrm{km} / \mathrm{h}$ approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning to red, and she is 28 $\mathrm{m}$ away from the near side of the intersection (Fig. 51). Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 $\mathrm{m}$ wide. Her car's maximum deceleration is $-5.8 \mathrm{m} / \mathrm{s}^{2}$whereas it can accelerate from 45 $\mathrm{km} / \mathrm{h}$ to 65 $\mathrm{km} / \mathrm{h}$ in 6.0 $\mathrm{s}$ . Ignore the length of her car and her reaction time.

The woman should stop the car.

Physics 101 Mechanics

Chapter 2

Describing Motion: Kinematics in One Dimension

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

University of Washington

Simon Fraser University

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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so we know that the car's initial speed is the initial. This is equaling 45 kilometers per hour. We're going to use the conversion one meter per second for every 3.6 kilometers per hour. This is giving us 12 and 1/2 meters per second. Ah, we can say that for case one. We're trying to stop before the intersection and our maximum deceleration would be equal to negative 5.8 time negative, 5.8 meters per second squared. So we can say Can the car stop in within 28 meters? So we can say that velocity final squared equals loss Initial squared plus two times a doubt tow X. Let's solve for Delta acts. We know that velocity final squared would be equal to zero. Therefore, this would be equal to velocity Initial squared divided by two times A. This is giving us negative 12.5 meters per second quantity squared, divided by two times negative 5.8 meters per second squared. This is giving us 13.5 meters and so we can say that Yes, she stopped the current time where 13 0.5 meters is of course less than 28 meters now for case too. Case too were trying to cross the intersection. So we can, uh we know that the acceleration of the car we can solve for this acceleration of the car is gonna be equal to 55 kilometers per hour, minus 45 kilometers per hour divided by 6.0 seconds. And the murder again multiplying by one meter per second, divided by 3.6 kilometers per hour. And we find that the acceleration of the car would be 0.959 rather 0.959 9 to 559 meters per second squared. And so at this point, um, we need to get through the intersection where Delta X equals 43 meters in two seconds before the light turns red. So we can say that Delta X equals V X initial T plus 1/2 times 80 square. This is gonna equal 12.5 meters per second, multiplied by 2.0 seconds plus 1/2 times 0.9 to 559 times 2.0 seconds. Quantity squared. And we find that Delta X is giving us 26.9. This is going to be late meters, so No. Uh, the car should stop before the intersection. That is the end of the solution. Thank you for watching.

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