This graph could represent a race of some sort where the contestants were all lined up at the starting line (although, at these speeds it must have been a race between tortoises). Since each of these graphs has its intercept at the origin, each of these objects had the same initial position. Thus velocity corresponds to slope and initial position to the intercept on the vertical axis (commonly thought of as the "y" axis).
(The independent variable of a linear function is raised no higher than the first power.)Ĭompare the position-time equation for constant velocity with the classic slope-intercept equation taught in introductory algebra. Even a straight line is called a curve in mathematics.) This is to be expected given the linear nature of the appropriate equation. (Any kind of line drawn on a graph is called a curve. Note first that the graphs are all straight. Three different curves are included on the graph to the right, each with an initial position of zero. Let's begin by graphing some examples of motion at a constant velocity. Graphs of motion come in several types depending on which of the kinematic quantities (time, position, velocity, acceleration) are assigned to which axis. Graphs are often the best way to convey descriptions of real world events in a compact form. Sometimes you need a picture to show what's going on - a mathematical picture called a graph. Since, as I rightly pointed out, "no object has ever traveled in a straight line with constant acceleration anywhere in the universe at any time" these equations are only approximately true, only once in a while.Įquations are great for describing idealized situations, but they don't always cut it. You should recall that the three (or four) equations presented in that section were only valid for motion with constant acceleration along a straight line. Think back to the previous section on the equations of motion. When it comes to depth, nothing beats an equation. All of these relationships can now be written in a single equation. Galileo's description of an object moving with constant speed (perhaps the first application of mathematics to motion) required one definition, four axioms, and six theorems. Equations can easily contain the information equivalent of several sentences. Modern mathematical notation is a highly compact way to encode ideas. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Paul Peter Urone, Roger Hinrichs Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format,
Want to cite, share, or modify this book? This book uses the In Two-Dimensional Kinematics, we apply concepts developed here to study motion along curved paths (two- and three-dimensional motion) for example, that of a car rounding a curve. In this chapter, we examine the simplest type of motion-namely, motion along a straight line, or one-dimensional motion. Such considerations come in other chapters. In one-dimensional kinematics and Two-Dimensional Kinematics we will study only the motion of a football, for example, without worrying about what forces cause or change its motion. The word “kinematics” comes from a Greek term meaning motion and is related to other English words such as “cinema” (movies) and “kinesiology” (the study of human motion). Our formal study of physics begins with kinematics which is defined as the study of motion without considering its causes. An understanding of acceleration, for example, is crucial to the study of force.
Questions about motion are interesting in and of themselves: How long will it take for a space probe to get to Mars? Where will a football land if it is thrown at a certain angle? But an understanding of motion is also key to understanding other concepts in physics. And even in inanimate objects, there is continuous motion in the vibrations of atoms and molecules. When you are resting, your heart moves blood through your veins.
Everything from a tennis game to a space-probe flyby of the planet Neptune involves motion. Objects are in motion everywhere we look.
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