Unit 1: Motion and its Unit 1: Motion and its ApplicationsApplicationsKinematics

the language of motionthe language of motionmechanics 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 vectorsscalars and vectorsthe 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

QuantitySymbol Vector

QuantitySymbol

distance (m) d position d

speed (m/s) v displacement Δd

acceleration (m/s2)

a velocity v

time (s) t acceleration a

distance, displacement, distance, displacement, positionpositiondistance 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:

displacementdisplacementΔ “delta” = ‘change in’displacement is a change in position

to calculate displacement◦Δd = dfinal – dinitial

to calculate total displacement◦ΔdT = Δd1 + Δd2

◦if the displacements are in opposite directions, convert the ‘sign’ so they are the same

speed and velocityspeed and velocityspeed how fast an object is movinginstantaneous 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)

vav = Δd = d2 – d1 Δt t2 - t1

Note: speed is the rate at which distance changes while velocity is the change in position (displacement) divided by the time taken

exampleexampleConsider 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 motiontypes of motionuniform 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)