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, 2.36M subscribers 283K views 6 years ago Classical Physics Everyone loves graphs Especially when they give us so much information about the motion of an object. 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. The slope of this line will give us the acceleration.Objects are in motion everywhere we look. If the acceleration is constant the v-t graph will be a straight line. The slope of the tangent to a v-t graph at one point in time will give instantaneous acceleration in the case where there is non uniform (changing) acceleration. Using a method similar to deriving velocity from distance-time graphs, we can obtain values of acceleration from velocity-time graphs. V inst = v or, using the slope equation we calulte the slope of the tangent (the red line): To obtain the instantaneous velocity, that is, the velocity at one instant (one point in time - say at exactly t 1), one must take the slope of the tangent line that just touches the curve at that point. This gives us the average velocity between the time interval from t 1 -to- t 2 Slope (of secant line) = Delta d / Delta t The slope of the secant line (the line that cuts the curve at the two intersecting points (d 1,t 1 and d 2, t 2) can be calculated by the usual slope method: To obtain the average velocity between two points in time (say t 1 and t 2) we can draw the secant line between these two points and calculate the slope of the secant line. It is sufficient to say, however that we can still obtain some useful information by relying on graphical analysis techniques. To analyze this function properly one would need to take the first derivative of the function using Calculus. We know that the velocity is changing as time goes on because the slope of this line is not constant and the function (of the form y = ax 2 + bx + c) is an increasing function. This graph illustrates the relationship between the position and the time for an object whose velocity is changing with time.

Uniformly Accelerated Motion - Variable Speed

We note that 'm', the slope of the line (of the form, y = mx + b) is constant and can be calculated by several methods.ī. The slope m of the position-time graph gives the velocity of the object even when the relation between the position (d) and the time (t) is not a straight line. This is a typical graph of the relationship between position and time for an object moving at constant speed. Uniform Motion - Constant Speed - no acceleration

Graphical analysis of motion physics