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Fundamentals of Physics at University of Maryland: Motion and Velocity Analysis

Explore the foundational concepts of motion, coordinates, and velocity in physics at the University of Maryland. Topics include dimensional analysis, space coordinates, vectors, displacement vs. distance, average and instantaneous velocity, and graphing velocity. Understand how time, position, and direction play crucial roles in describing motion mathematically. Enhance your comprehension of fundamental physics principles through examples and problem-solving activities.

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Fundamentals of Physics at University of Maryland: Motion and Velocity Analysis

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  1. Physics 121:Fundamentals of Physics I September 8, 2006 University of Maryland

  2. Announcements / Reminders • Next homework is available on WebAssign • Free WebAssign use expires next Wednesday! • Tutorials (Discussion Sections) and Labs will begin meeting next week University of Maryland

  3. Outline • Example Dimensional Analysis Problem • Describing Motion: • Coordinates in space and time • The idea of velocity • average velocity • instantaneous velocity • graphing velocity University of Maryland

  4. Dimensional Analysis • In the following equation, determine what the dimensions of g have to be in order for the equation to be physically meaningful: • where [v]=L/T, [x]=L and [m]=M • L is length • M is mass • T is time University of Maryland

  5. Describing Motion: Space • Coordinates — telling where something is • What do we need to do to specify the location of something so someone else can find it? • Note the difference between “length” or “distance” and “position” • Representing a position mathematically. University of Maryland

  6. Coordinates and Vectors • Set up a coordinate system • Pick an origin • Pick 3 perpendicular directions • Choose a measurement scale • Each point in space in then specified by three numbers: the x, y, and z coordinates. • The position vector for a particular position is an arrow drawn from the origin to that position. University of Maryland

  7. Motion along a straight line (1-d coordinates) • We specify which direction we are talking about by drawing a little arrow of unit length in the positive direction. • We specify that we are talking about this arrow in symbols by writing • A position a distance x from the origin is written • Note that if x is negative, it means a vector pointing in the direction opposite to University of Maryland

  8. Describing Motion: Time • Time — if we’re to describe something moving we need to tell when it is where it is. • Time is a coordinate just like position • We need an origin (when we choose t = 0) • a direction (usually times later than 0 are +) • a scale (seconds, years, millennia) • Note the difference between • clock reading • a time interval This is like the difference between position and length! University of Maryland

  9. Writing the math • Position at a clock time t:(if we want to emphasizethe direction) • Position at a clock time t:(if we don’t) • Change in position betweentwo times (t1 and t2): • Time interval: University of Maryland

  10. Graphing Position • Describe where something is in terms of its coordinate at a given time. University of Maryland

  11. Displacement • The displacement is the total change in position. • If you make one change and then go back, it could cancel out the first change. University of Maryland

  12. Displacement Isn’t Distance • The displacement of an object is not the same as the distance it travels • Example: Throw a ball straight up and then catch it at the same point you released it • The distance is twice the height • The displacement is zero University of Maryland

  13. C A B x 0 5 10 15 feet Below is shown a straight track along which a toy train can move. If the train moves from point A to point C and then back to point B, what is its resulting displacement (in feet)? • 2 feet • 3 feet • 5 feet • 12 feet • None of the above

  14. Average Velocity • We need to keep track not only of the fact that something has moved but how long it took to get there. • Define the average velocity by University of Maryland

  15. Uniform motion • If an object moves so that it changes its position by the same amount in each unit of time, we say it is in uniform motion. • This means the average velocity will be the same no matter what interval of time we choose. University of Maryland

  16. Instantaneous velocity • Sometimes (often) an object will move so that it is not in uniform motion. Sometimes it moves faster, sometimes slower, sometimes not at all. • We want to be able to describe this change in motion also. • If we consider small enough time intervals, the motion will look uniform — for a little while at least. University of Maryland

  17. Graphing Velocity • An object in uniform motion has constant velocity. • This means the instantaneous velocity does not change with time. Its graph is a horizontal line. • You can see this by putting your mind in “velocity mode” and running a mental movie. University of Maryland

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