Ch. 2 - 3

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14 Νοε 2013 (πριν από 3 χρόνια και 5 μήνες)

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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