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
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)
0
0
1
3
2
6
3
9
4
12
5
15
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)
0
2
1
4
2
6
3
8
4
10
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:
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
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