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# Section02 - Physics 204A Class Notes Section 2 Motion In...

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Physics 204A Class Notes 2-1 Section 2 - Motion In One Dimension Section Outline 1. The Definition of Position 2. The Definition of Displacement 3. The Definition of Average Velocity 4. The Definitions of Instantaneous Velocity and Speed 5. The Definitions of Average Acceleration and Instantaneous Acceleration 6. The Calculus of Motion 7. The Special Case of Constant Acceleration 8. Freely Falling Bodies 9. Non-constant Acceleration Let’s start to answer the question, “What do objects do?” Whether the object is an atom, a baseball, or a star, they all move. So, we need to be able to thoroughly describe motion. We will not worry about the cause of the motion – that will come later. The description of motion is called “Kinematics.” We’ll begin by very carefully defining the words and ideas we’ll use. 1. The Definition of Position The first step is to describe the location of the object is to know where it is. The Definition of Position: The location of an object with respect to a coordinate system. The location of an object is meaningless unless it is referenced to something. In physics, that something is called a coordinate system or frame of reference. You can choose any coordinate system that you would like, however, you must always indicate which one you have chosen. We’ll discover that there are distinct advantages to using certain coordinate systems as we go further. For now, we’ll usually just the describe the position as the location along the x-axis as shown above. Rewritten mathematically, The Definition of Position: x 2. The Definition of Displacement Physics wouldn’t be very interesting if objects stayed in one place. So the next thing we need to define is changes in location. The Definition of Displacement: A change in position. Rewritten mathematically, The Definition of Displacement: " x # x f \$ x i x y x x y x f x i

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Physics 204A Class Notes 2-2 Example 2.1: At the right is a graph of my last trip to Los Angeles. The origin is at Chico. Find (a)my position at t=2h, (b) my position at t=8h, (c) my displacement during these 6h and (d)my total displacement. In this example, the coordinate system has been chosen for us. The origin is at Chico and the x-axis points toward Los Angeles. (a)We can get position values by reading the graph, x i = 110mi. (b)Again, reading the graph, x f = 375mi. (c)Using the definition of displacement, ! x " x f # x i = 375 # 110 \$ x = 265mi. (d)Estimating from the graph, using the definition of displacement, " x # x f \$ x i = 495 \$ 0 % x ot = 495mi. 3. The Definition of Average Velocity The next step is to describe how quickly the location is changing (How fast is it going?) The Definition of Average Velocity: The average rate of displacement. Mathematically, The Definition of Average Velocity: v ! " x " t = x f # x i t f # t i Example 2.2: Find my average velocity (a)during the interval from t = 2h to t = 8h and (b)for the entire trip.
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Section02 - Physics 204A Class Notes Section 2 Motion In...

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