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Ch. 2 - 3

Ch. 2 - 3. Displacement, Velocity, and Acceleration. Vocabulary . Mechanics – the study of the motion of objects Kinematics – Describing the motion of objects with words, diagrams, graphs and mathematical equations. Vocabulary.

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Ch. 2 - 3

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  1. Ch. 2 - 3 Displacement, Velocity, and Acceleration

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

  3. 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

  4. 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!)

  5. Calculating Displacement

  6. 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:

  7. Calculating Velocity

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

  9. 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:

  10. 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:

  11. Position vs. Time Graphs • Position on y-axis • Time on x-axis • Example with constant velocity • Slope of line =

  12. Position vs. time graphs - examples

  13. Velocity vs. Time graphs • Velocity on y-axis; time on x-axis • Example – constant acceleration: • Slope of velocity vs. time graph =

  14. Velocity vs. Time Graph - examples

  15. 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

  16. Equations of Kinematics • Velocity with average accel. equation

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

  18. Equations of Kinematics • Final velocity squared

  19. Kinematics Example: Dimensional Analysis

  20. Kinematics Example:

  21. Kinematics Example:

  22. 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:

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

  24. Free Fall ex: Object is dropped

  25. Free Fall ex: Obj. is thrown upward

  26. Free Fall ex: Obj. is thrown downward

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