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Sketch the $v$ vs, $t$ graph for the object whose displacement as a function of time is given by Fig. $36 .$

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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

Hope College

University of Winnipeg

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.

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.

02:31

(III) Sketch the $\upsilon…

03:27

(II) Construct the $v$ vs.…

10:20

The graph shows $x(t)$ for…

04:17

An object moves in a strai…

05:11

For the velocity-versus-ti…

02:18

Find the displacement-time…

06:35

02:03

Objects $A, B . C$ move al…

03:17

Displacement from a veloci…

01:27

Figure shows the displacem…

09:48

The velocity-time graph of…

Okay, This is a graphing problem and were given a plot of position versus time. So this is X, uh, it meters. And this is time in seconds, and I'll just roughly sketch out what it looks like. So we have as important points. I think about 20 seconds and 30 seconds. 40 seconds. Um, looks like this kind of something like that, um, and a couple techniques I'm going to use. So we want to find velocity versus time based on this. Okay, this is time and this philosophy and what I'm gonna do to figure out the velocity if we remember that velocity, you can say this is the derivative of position, the time derivative. And so that means that the slope of this graph, any point we can approximate it is gonna be the velocity. So we can think of the velocity first is constant all the way through here. Then it starts to increase up to this point around 30 seconds and then stressed to decrease until it gets to zero here just before 40 seconds. And then a decreases again. And then it started slowly. Starts to increase a bit here. So that's a way to figure out the velocity any one point in time and in general. So let's break this into section. So 0 to 20 seconds, we have a constant slope for the position versus time. So that means we're gonna have a constant velocity and our velocity in that time. I'm just gonna estimate, uh, I'll say Delta X ever dealt t for a larger range. It's gonna be 20 meters vs Helen that take, let's say, about 12 seconds and so that's going to give us 120.6 meters per second. So say here at 0.6 for the 1st 20 seconds, our velocity is a constant. And then from 20 to 30 seconds, it starts to increase. And it 40 seconds 6 30 seconds, 40 seconds. I need to make this a little longer. Ah, At 40 seconds or just before 40 seconds, this position versus time flattens off. So we know at that point our velocity is gonna be zero, because our position is not changing. So we have to get to zero in here at some point. Okay? Ah, so from 20 to 30 we're gonna increase, and then we're gonna start decreasing till we get to zero. So with 30 seconds, I think it looks like about a slope of one. So I'm going to say here one meter per second one day, right time here. This is meters per second at one meter per second. At 30 seconds, we're gonna have a velocity of one meter per second. So this is gonna start increasing here, and then it starts to decrease a little better. It's going to start to decrease down until we have to hit zero here. Now, after that, until about 45 seconds. Say 45 50 It's gonna decrease, decrease all the way down here until we hit about 45 seconds. And then at that point, it starts to increase. And by that I mean get less negative because we're going into the negatives now. And at 45 seconds, it starts to get less and less negative until we get to 50. Because the if you know more about calculus, so go a little deeper into that. This has to do with Khan cavity of the graph. And at this point right here, it's switching. Also it this Ah, this point at this point, that's why I ended up picking 2030 for you 45 seconds is cause that's where the con cavity of the graph is changing, and we can figure out the velocity from that. But if you're not too comfortable with thinking about derivatives and calculus than we can, just look at how the position is changing and important things to know our when the position is linear, position versus time is linear or velocity is constant. And when it looks like the position versus time, get rid of some of these lines here when it looks like position versus time is flattening out. So, like right here, that's where velocity is zero. So I plotted those two points. This is where the velocity is zero. And for this section here, the velocity is constant. In between those two, we just have to fill in. So this point, it's where the velocities or the position versus time is the steepest. So that's the greatest philosophy, and then you just have to plot a few more points and then connect the dots. And that's the intuitive way of had term physician versus time into velocity. And if you took the derivative of the position versus time graph it every point and ended up just mapping it onto this graph. You get something that looks pretty similar.

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