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A Toyota Prius driving north at 65 $\mathrm{mph}$ and a $\mathrm{VW}$ Passat driving south at 42 $\mathrm{mph}$ are on the same road heading toward each other (but in different lanes). What is the velocity of each car relative to the other (a) when they are 250 $\mathrm{ft}$ apart, just before they meet, and (b) when they are 525 $\mathrm{ft}$ apart, after they have passed each other?

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a) 107 $\mathrm{mph}$b) 107 $\mathrm{mph}$

Physics 101 Mechanics

Chapter 2

Motion along a Straight Line

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

University of Michigan - Ann Arbor

Hope College

University of Sheffield

University of Winnipeg

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.

03:07

A Toyota Prius driving nor…

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05:31

Two cars are heading towar…

06:16

Car $A$ is driving east to…

01:49

Two cars travel in the sam…

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06:34

(a) One car leaves a given…

a. One car leaves a given …

04:48

Two cars leave an intersec…

Cars $A$ and $B$ are both …

02:49

Two cars are 200 mi apart …

02:45

Two cars are 238 mi apart …

04:26

Car $A$ is driving south, …

01:22

Two cars are driving towar…

uh, little velocity addition. So we know that velocity. The prospect of e e did not arc. There's a creditable velocity off with respect to read of Luke. He stands for Toyota, respectively. From this equation, we can, right. Let the velocity off to your dove in respect of the other car. Now, from here, we can simply like the white component off the secretion. Still, we have with the blue. Maybe it's less rid of blue. Confident off. Why? Since we're taking the confidence we don't I need two very about Victor sign. We just need to take the magnitudes, uh, taking get off the signs for positive. I remember it in my direction. Confident now this value is given to the 65 Meet our velocity ofthe respect on velocity of the other car With respect to our is 40 to meet upon our But this is no do itself. And this is stores not, and we have taken not to be positive to south is negative. So there should be a negative sign when we apply this and this aggression. And this gives no that a letter velocity between the two cars to be positive ones in a seven meter. This means that related to the vida blue. The Toyota is traveling not because this is positive. So cheap point to. Well, it's not So the bad guys traveling north at 100 7 meter people are on DH if you want to find velocity off on the vida blue with respect to Toyota in the right direction because their boat traveling, Uh, not our South. So velocity of reader blew with respect to the Toyota will get in 100 7 meet up around where they shouldn't be, do it south, and so it should have been a good site. This comes from the fact that this velocity is, in fact, negative relative velocity. No, you're respected. Let me just separated from the rest of the question.

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