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Chapter 2
What kinds of motion can you describe?
How do you know that an object has moved? Be
specific.
Let’s start at the very beginning… Straight Line
Motion.
A series of images showing the positions of a moving
object at equal time intervals is called a motion
diagram.
A particle model is a simplified version of a motion
diagram in which the object in motion is replaced by a
series of single points.
Coordinate Systems
Tells you the location of the zero point of the variable
you are studying and the direction in which the values of
the variable increase.
The origin is the point at which both variables have a
value of zero
Position can be represented by drawing an arrow from
the origin to the point representing the object’s new
location
The length of the arrow indicates how far the object is from
the origin or the distance.
Vectors
Scalars
Have magnitude (size) and
Only have magnitude
direction
Require the use of
VECTOR ADDITION to
determine resultant
vector
Can be added or combined
using standard rules of
addition and subtraction
Vector
Scalar
Displacement
Distance
Velocity
Speed
Acceleration
Time
Force
Temperature
You will need a ruler, protractor, and pencil
Draw a coordinate system (small) as your origin
Draw an arrow with the tail at the origin and the head
pointing in the direction of motion.
The length of the arrow should represent the distance
traveled.
Add the second vector using the head to tail method.
Measure resultant magnitude and direction.
Add vectors using “head to tail” method.
Pictures do not need to be drawn to scale. No need for
a ruler and protractor.
Use Pythagorean Theorem and SOHCAHTOA to solve
for resultant vectors ONLY when RIGHT TRIANGLES
are formed. a 2 b 2 c 2
If not right triangles, use Law of Sines and Law of
Cosines to solve for resultant vectors.
sin A sin B sin C
a
b
c
c a b 2abcos
2
2
2
The difference between two times is called a time
interval and is expressed as t t f ti
i and f can be any two time variables you choose
(according to each problem)
A change in position is referred to as displacement.
d d f di
Distance ≠ Displacement
Displacement is the shortest distance from start to finish
or “as the crow flies”
Draw the following:
10m East
-10m
10m North + 12m West
Every vector has x- and y- components.
In other words, a vector pointing southwest has both a
south (y) and west (x) component.
Vectors can be “resolved into c0mponents”.
Use SOHCAHTOA to find the x- and y- components
Break EACH vector into x- and y- components.
Assign negative and positive values to each component
according to quadrant rules. For instance, south
would have a negative sign.
Add the x- column. Add the y- column.
Use Pythagorean Theorem to determine the final
displacement magnitude.
Use SOHCAHTOA to find the final displacement
direction.
Plot time on the x-axis and position on the y-axis
Slope will indicate average velocity
Use this website for extra help.
http://www.physicsclassroom.com/Class/1DKin/U1L3a.cfm
Shape of Slope
Interpretation
Linear
Constant speed
(can be positive or negative)
Parabolic
Speeding up
Hyperbola
Slowing down
Average velocity is defined as the change in position,
divided by the time during which the change occurred.
On a position vs. time graph, both magnitude and
relative direction of displacement are given. A
negative slope indicates an object moving toward the
zero position.
d d f di
v
t
t f ti
Speed simply indicates magnitude
or “how fast.”
Velocity indicates BOTH
magnitude and direction. In
other words velocity tells you “how
fast” and “where.”
When solving for average velocity, two points for
position and time are chosen for comparison.
Individual changes in speed could have taken place
within those intervals.
Instantaneous velocity represents the speed and
direction of an object at a particular instant.
On a position-time graph, instantaneous velocity can
be found by determining the slope of a tangent line on
the curve at an given instant.
So far, we have looked at motion diagrams, particle
models, and graphs as a means of representing
motion.
Equations are also quite useful.
Based on the equation y=mx +b, one final equation
will be derived in this chapter.
d vt di
d = final position
v = average velocity
t = time interval
di = initial position (based on y-intercept if using a graph)
Read Chapter 1! You will reinforce all of these
concepts, drill them into your head and see more
examples than I have given here.
Visit www.physicsclassroom.com This website offers
great explanations of physics concepts.
Watch this video. It is a little boring but very helpful.
http://www.youtube.com/watch?v=4J-mUek-zGw