Ch 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  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

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!)

Calculating Displacement

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:

Calculating Velocity

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

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:

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:

Position vs. Time Graphs  Position on y-axis  Time on x-axis  Example with constant velocity  Slope of line = Time (s)Position (m)

Position vs. time graphs - examples

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)

Velocity vs. Time Graph - examples

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

Equations of Kinematics  Velocity with average accel. equation

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

Equations of Kinematics  Final velocity squared

Kinematics Example: Dimensional Analysis

Kinematics Example:

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:

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

Free Fall ex: Object is dropped

Free Fall ex: Obj. is thrown upward

Free Fall ex: Obj. is thrown downward