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Unformatted text preview: Chapter 6 One-Dimensional Motion (Motion Along a Line): Definitions and Mathematics 30 6 One-Dimensional Motion (Motion Along a Line): Definitions and Mathematics A mistake that is often made in linear motion problems involving acceleration, is using the velocity at the end of a time interval as if it was valid for the entire time interval. The mistake crops up in constant acceleration problems when folks try to use the definition of average velocity t x = v in the solution. Unless you are asked specifically about average velocity, you will never need to use this equation to solve a physics problem. Avoid using this equationit will only get you into trouble. For constant acceleration problems, use the set of constant acceleration equations provided you. Here we consider the motion of a particle along a straight line. The particle can speed up and slow down and it can move forward or backward but it does not leave the line. While the discussion is about a particle (a fictitious object which at any instant in time is at a point in space but has no extent in spaceno width, height, length, or diameter) it also applies to a rigid body that moves along a straight line path without rotating, because in such a case, every particle of the body undergoes one and the same motion. This means that we can pick one particle on the body and when we have determined the motion of that particle, we have determined the motion of the entire rigid body. So how do we characterize the motion of a particle? Lets start by defining some variables: t How much time t has elapsed since some initial time. The initial time is often referred to as the start of observations and even more often assigned the value 0. We will refer to the amount of time t that has elapsed since time zero as the stopwatch reading. A time interval t (to be read delta t) can then be referred to as the difference between two stopwatch readings. x Where the object is along the straight line. To specify the position of an object on a line, one has to define a reference position (the start line) and a forward direction. Having defined a forward direction, the backward direction is understood to be the opposite direction. It is conventional to use the symbol x to represent the position of a particle. The values that x can have, have units of length. The SI unit of length is the meter. (SI stands for Systeme International, the international system of units.) The symbol for the meter is m. The physical quantity x can be positive or negative where it is understood that a particle which is said to be minus five meters forward of the start line (more concisely stated as x = 5 m) is actually five meters behind the start line. Chapter 6 One-Dimensional Motion (Motion Along a Line): Definitions and Mathematics 31 v How fast and which way the particle is goingthe velocity 1 of the object. Because we are considering an object that is moving only along a line, the which way part is either...
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