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Unformatted text preview: Chapter 2: Kinematics In One Dimension 1. Displacement 2. Speed and Velocity 3. Average Velocity 4. Instantaneous Velocity 5. Average and Instantaneous Acceleration 6. Equations of Kinematics for Constant Acceleration 7. Applications of the Equations of Kinematics 8. Freely Falling Objects 9. Graphical Analysis of Velocity and Acceleration 10. Relative Velocity along a Straight Line We start studying mechanics , i.e., the relationship between force, matter, and motion. Kinematics is a discipline that describes motion using mathematical methods. Dynamics is a discipline that describes the relationship between motion and its causes. DISPLACEMENT AND AVERAGE VELOCITY Consider displacement of a car along a straight line, which we arbitrarily define as the xaxis. The car’s average velocity is a vector quantity whose x component is ( x 2 – x 1 )/( t 2 – t 1 ) = 258 m/3 s = 86 m/s. All other components are zero. In physics usually change in a parameter, e.g., x 2 – x 1 , is expressed as ∆ x (delta x ). Using this notation, we can write , av x x v t ∆ = ∆ ∆ x or ∆ t always denote the final value minus the initial value. The average velocity can also be negative, as in the example shown below. 2 1 , 2 1 19 277 258 25.8 / 16 6 10 av x x x m m m v m s t t s s s = = = =  (2.1) So, the average velocity tells us about the average velocity and the direction of the motion. It doesn’t contain any information if the velocity has been constant or variable. The direction is not an absolute entity; it depends on how we define the positive direction of the x axis. Example: You swim the total length of the pool in 24 s, and then swim back in 48 s. Find the average velocity of a) forward swim, b) backward swim, and c) the total swim. , , , 50 2.08 / 24 50 1.04 / 48 / 72 av forward av back av total m v m s s m v m s s m v m s s = = = =  = = The difference between velocity and speed is that the speed is defined like velocity but is a scalar quantity, it doesn’t depend on the direction of motion. So the overall average speed in the above example would be 100 m/72s = 1.39 m/s Graphical Representation of Motion along a Straight Line When the position changes with time, we say it in mathematical language that the position (in this case, the coordinate x ) is a function of time ( t ). Graphically it is presented like this: By definition, v av,x = ∆ x / ∆ t . This is simply the slope of the graph. When the slope is the same for any time interval, it means the velocity is constant. But the velocity can be variable, non constant, as shown in the graph below. Note that while the object moves along a straight line, the shape of the graph x = f ( t ) can acquire any shape. This means the graph doesn’t reflect the path of the object, but only its velocity....
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This note was uploaded on 09/21/2011 for the course PHY 1500 taught by Professor Staff during the Spring '09 term at University of Central Florida.
 Spring '09
 Staff

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