Unit 1: Motion and its Applications Kinematics

the language of motion mechanics  the study of objects in motion dynamics  the study of why things move kinematics  branch of mechanics concerned with describing the motion of objects ◦ motion can be described using words, pictures, graphs, and numbers

scalars and vectors the mathematical quantities used to describe motion can be divided into 2 categories: scalars  a quantity described by a magnitude (number and unit) vectors  quantity described by a magnitude and direction [in square brackets]

when describing direction, “up/north/east/rightward/forward” are considered positive directions (+) “down/south/west/left/back” are negative (-) Scalar Quantity SymbolVector Quantity Symbol distance (m)dposition dd speed (m/s)vdisplacement ΔdΔd acceleration (m/s 2 ) avelocity vv time (s)tacceleration aa

distance, displacement, position distance  how much ground the object has covered during its motion (scalar) position  the location of an object relative to a reference point (vector) displacement  the object’s overall change in position (vector) calculate distance and displacement for this path:

displacement Δ “delta” = ‘change in’ displacement is a change in position to calculate displacement ◦ Δ d = d final – d initial to calculate total displacement ◦ Δ d T = Δ d 1 + Δ d 2 ◦ if the displacements are in opposite directions, convert the ‘sign’ so they are the same

speed and velocity speed  how fast an object is moving instantaneous speed  speed at a specific moment in time (speedometer) constant speed  instantaneous speed is maintained for a long period of time (cruise control) average speed  the average of all instantaneous speeds (total distance divided by total time)

speed is a scalar quantity (v)  velocity is a vector quantity (v) v av = Δ d = d 2 – d 1 Δ t t 2 - t 1 Note: speed is the rate at which distance changes while velocity is the change in position (displacement) divided by the time taken

example Consider the following path once again: The subject walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. determine the average speed determine the average velocity

types of motion uniform motion  at a constant speed in a straight line (simplest type of motion an object can undergo besides rest) non-uniform motion  the object’s speed changes or the object does not travel in a straight line (accelerated motion)