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Figure 50 is a position versus time graph for the motion of an object along the $x$ axis. Consider the time interval from A to B. (a) Is the object moving in the positive or negative direction? (b) Is the object speeding up or slowing down? (c) Is the acceleration of the object positive or negative? Next, consider the time interval from D to E. (d) Is the object moving in the positive or negative direction? (e) Is the object speeding up or slowing down? (f) Is the acceleration of the object positive or negative? (g) Finally, answer these same three questions for the time interval from $C$ to $D$ .

a) Negative.b) Speeding up.c) Negatived) Positivee) Speeding up.f) Positiveg) So, The Acceleration, Acceleration and the direction of movement is all zero.

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

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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.

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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 this question is all about interpreting a position for his time graph, and there are numbers, but we don't really need that because it's just qualitative for now, um so the first intervals from A to B, which looks a little bit like this. And first we want to know, uh is the object moving in the positive or negative direction and, well, it's pretty obvious it's going from here two here. So that's, you know, moving backwards cause this this lower. So it's with me in the negative direction. The position is going to be easy to get from a position versus time. Graph the velocity. We don't actually want another Veloster you want to know, is the object speeding up or slowing down? And the rate of change is actually increasing here. Even though it's getting more negative, it's still increasing. So when we start here, if we think kind of about the derivative ah, here, it's not really moving because it's ah, flat rate of change. And then here the rate of change is increasing, Increasing, increasing now here is really big, even though it's still moving backwards, it is speeding up, and that moves into the next part where we want to know is the acceleration positive or negative? Well, the velocity is going from zero and increasing in the negative direction. So our acceleration for this first part is gonna be negative. And now Ah, Interval from D T E down here. Well, it's pretty much the opposite of the first part. The object is speeding up. Yes, it's Ah, it's moving in the positive direction now going from here to here. And it's speeding up, of course, going from pretty flat to increasing. Like this, uh, speeding up so speeding up in the positive direction of this time. So our acceleration for this section of the graph is positive. And for the last section, which is right here, it's flat. So the objects not moving because it's maintaining the same position. If it's in the same position than it's also not speeding up or slowing down and speeding up or slowing down, then it has zero acceleration, so is not positive or negative. So whenever you have a flat line, I'm on a position versus time graph. Everything in position lost exploration is gonna be zero

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