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A person is walking briskly in a straight line, which we shall call the $x$ axis. Figure 2.40 shows a graph of the person's position $x$ along this axis as a function of time $t$ (a) What is the person's displacement during each of the following time intervals: (i) between $t=1.0 \mathrm{s}$ and $t=10.0 \mathrm{s},$ (ii) between $t=3.0 \mathrm{s}$ and $t=10.0 \mathrm{s},($ iii) between $t=2.0 \mathrm{s}$ and $t=3.0 \mathrm{s}$ and (iv) between $t=2.0 \mathrm{s}$ and $t=4.0 \mathrm{s} ?$ (b) What distance did the person move from (i) $t=0$ s to $t=4.0 \mathrm{s}$ , (ii) $t=2.0 \mathrm{s}$ to $t=4.0 \mathrm{s},$ and (ii) $t=8.0 \mathrm{s}$ to $t=10.0 \mathrm{s} ?$

$x_{\mathrm{net}}=4.0 \mathrm{m}$$x_{\mathrm{nct}}=6.0 \mathrm{m}$$x_{\mathrm{net}}=-1.0 \mathrm{m}$$x_{\text { net }}=0.0 \mathrm{m}$$d_{\mathrm{nat}}=4 \mathrm{m}$$d_{\mathrm{nat}}=2 \mathrm{m}$$d=0 \mathrm{m}$

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

Amber M.

January 26, 2021

can you explain how you got the distance answers please?

Cornell University

Rutgers, The State University of New Jersey

University of Sheffield

University of Winnipeg

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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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Okay, so from the graph Ah, we can say that X at one second ex two seconds except three seconds. So we can simply find the position at each of these points in time. So there's going to be 1.0 meters, zero meters negative, 1.0 meters. Is there a meters, 6.0 meters and then 6.4 meters. So for party, they simply want you to find the Delta X. They have four parts. So the first part of party is finding the total displacement between one second and 10 seconds. So you simply do eight eight to the 10 seconds minus eight at one second. And this is equalling five meters. For a part two of party, we have Delta X between three and 10 seconds. So 10 seconds again minus X of three seconds. And this is equaling 7.0 meters For part three. We have felt acts equaling ex of three seconds except two seconds. So the total displacement between two seconds and three seconds, this is equaling negative 1.0 meters. So it actually went backwards and then for part for we have Delta X between two and four seconds. So force rather four seconds. Agent X at two seconds and this is equaling zero meters. This is again displacement. This is This is specific to displacement. And displacement is strictly defined as the distance from thie origin. So the origin must be defined. Um, and and for part B, excuse me. And for part B, we are finding the total distance. So for from zero seconds 24 seconds, we have three meters plus one meter and that equals four meters. And then for part two, we have two seconds too four seconds. And this is one plus Once that illegal tomb years. And then for part three, we have eight seconds to 10 seconds and this will be zero meters because here it's stays at eight out of X equaling six meters. So that's where during 88 seconds or 10 seconds. It doesn't move whatsoever. That is the end of the solution. Thank you for watching

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