# Ch. 2 - 3

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14 Νοε 2013 (πριν από 4 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