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(I) Figure 37 shows the velocity of a train as a function oftime. $(a)$ At what time was its velocity greatest? $(b)$ Duringwhat periods, if any, was the velocity constant? (c) Duringwhat periods, if any, was the acceleration constant?(d) When was the magnitude of the acceleration greatest?

a) 48 sb) $t=90 s$ to $t \approx 108 s$c) $t=0$ s to $t \approx 42 \mathrm{s}$ , $t \approx 65 \mathrm{s}$ to $t \approx 83 \mathrm{s}$ , $t=90 \mathrm{s}$ to $t \approx 108 \mathrm{s}$d) $t \approx 65 s$ to $t \approx 83 s$

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

Rutgers, The State University of New Jersey

University of Sheffield

McMaster 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.

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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 these answers are based on your interpretation of the graph, although they should be close. Uh, you might be You might have different definitions by a few seconds. So for party, they want us to find the greatest velocity. And because this is a philosophy versus time graph, we can say that, um, the greatest velocity would be found at the highest point of the grass. So we can say velocity Max. Good. Highest point. And we can set this roughly corresponds to a time of approximately equal to 48 seconds. So at 48 seconds, there is the maximum velocity for part B. The indication of a constant velocity on a velocity versus time graph would, of course, be a slope of zero. So when the slope is zero, this means that the velocity is not changing. And so we have a constant philosophy. This occurs so we could stay constant velocity, a slope equaling zero. Um, and this occurs between 90 seconds and 108 seconds That see, we have that the indication of a constant acceleration would be a constant slope. So this means that ah, constant acceleration would correspond to a linear slope. And here we have three periods where this occurs. So we have from zero seconds to 42 seconds. Uh, we have from 65 seconds, two, 83 seconds. And then we have from 90 seconds. Two again, 108 seconds. So a constant acceleration could also mean a zero acceleration as long as the acceleration itself isn't changing. So that's why the answer to be is also an answer to see and for party. We have that the, uh we want to find the where we get a maximum acceleration. So where on the graph is the acceleration, Max? And this is corresponds to where we have the greatest slope. So according to the scrap, the greatest slope occurs from against 65 seconds to 83 seconds. That is the end of the solution. Thank you for watching

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