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Ch. 2 - 3 Displacement, Velocity, and Acceleration

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Vocabulary Mechanics – the study of the motion of objects Kinematics – Describing the motion of objects with words, diagrams, graphs and mathematical equations

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Vocabulary Vector – a quantity (thing that can be measured) which contains both a size (magnitude) and direction. Ex: Scalar – a quantity which is completely described with a magnitude and has no associated direction Ex: - Some things are by nature a scalar or a vector, some are DEFINED to be a scalar or a vector

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Distance vs. Displacement vs. Position Distance – total path length travelled Scalar Displacement – length from starting to ending point. vector Points FROM starting point TO ending point Position – measured from origin (you set coordinate system!)

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Calculating Displacement

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Speed vs. Velocity Speed – “How fast” = distance / time Defined to be a scalar Equation for AVERAGE speed: Velocity – “how fast and in what direction” = DISPLACEMENT/time Defined as a vector (needs direction!) Equation for AVERAGE velocity:

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Calculating Velocity

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Acceleration “how quickly something speeds up” AND/OR “how quickly something changes direction” Equation for average acceleration: Direction of acceleration (in 1-D)

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Ticker-Tape Diagrams (aka particle diagrams) Dot represents the “center of mass” of the object Like a strobe light picture – equal intervals of time occur between each recorded dot Examples:

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Vector Diagrams (aka motion diagrams) Use a picture of the object (sometimes a dot) along with vectors to represent the motion of an object Length of arrow represents size of vector quantity Examples:

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Position vs. Time Graphs Position on y-axis Time on x-axis Example with constant velocity Slope of line = Time (s)Position (m) 00 13 26 39 412 515

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Position vs. time graphs - examples

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Velocity vs. Time graphs Velocity on y-axis; time on x-axis Example – constant acceleration: Slope of velocity vs. time graph = Time (s) Velocit y (m/s) 02 14 26 38 410

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Velocity vs. Time Graph - examples

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Velocity vs. Time graph – finding displacement Displacement = AREA between line and x-axis Area above the x-axis is positive displacement, area below is negative displacement Example

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Equations of Kinematics Velocity with average accel. equation

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Equations of Kinematics Displacement as area under position vs. time graph:

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Equations of Kinematics Final velocity squared

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Kinematics Example: Dimensional Analysis

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Kinematics Example:

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Free-Fall An object is in free fall if its motion is only being affected by gravity - air resistance is not a factor (negligible) - not being propelled by its own power source - generally assumed to be on earth, unless otherwise specified - can be going up OR down! Examples:

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Acceleration Due to Gravity Galileo’s Experiment (*demo/video demo) Acceleration due to gravity (on Earth) =

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Free Fall ex: Object is dropped

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Free Fall ex: Obj. is thrown upward

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Free Fall ex: Obj. is thrown downward

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