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Chapter 2
Representing Motion
Motion diagram- a series of images that
show the position of an object at specific time
intervals
Particle model- a simplified version of
the motion diagram in which the images are
replaced by single points.
When representing motion 2 types of quantities will be used:
• Scalars- Quantities that describe only size or
magnitude, they are just numbers without a specific
direction. Examples would be distance 87 km, 23 m,
400 ft
• Vectors- Quantities that describe both magnitude and
direction; examples 87 km east, 23m WSW, 400 ft south
 Vectors are represented by arrows that are drawn
to scale; When doing a problem involving vectors
choose a scale that will produce reasonable vectors
(5-10 cm)
80 m/s NE
N
120 m/s SE
66 m/s W
8 cm
6.6 cm
W
E
12 cm
Scale
1 cm = 10 m
S
Resultant vectors-the some of 2 or
more vectors
• A boy travels .5 km E to a store to pick up
bread and milk. The boy continues .2 km
E to deliver the milk and bread to his
What’s the
grandmother.
scale?
1cm=.1km
5 cm
2 cm
How far did the boy
travel?
7 cm
.7 km
Time intervals and displacements
• Two things are used to analyze motion.
– Time Intervals- the difference between 2
times Δt= tf - ti
Time Interval = final time - initial time
– Displacement- the change in position of an
object Δd= df – di
Displacement = final position minus initial
position
Distance vs. Displacement
• Distance and displacement are not
necessarily the same thing.
– Distance - How far you travel regardless of
direction.
– Displacement -"Change in position” this
not only takes into account distance but
direction as well
Example
Suppose a person moves in a straight line
from the lockers (at a position di = 1.0 m)
toward the physics lab (at position = 9.0 m) ,
as shown below
1.0 m
9.0 m
Δd= df – di = 9.0m – 1.0m = 8.0m
• In this example the distance would be
described as 8.0 m, but the displacement
would be described as 8.0 m to the right
Suppose the person turns around!
Δd= df – di = 1.0m – 9.0m = -8.0m
The answer is negative so the person
must have been traveling horizontally to
the left
What is the DISPLACEMENT for the entire trip?
0 m is the displacement because you have
ended at the same spot
What is the total DISTANCE for the entire trip?
The distance traveled is 16m
8m + 8m= 16m
Position-Time Graphs
• Graph used to show the position of an
object at a specific time.
– Y axis- displacement or position
– X-axis- time
Where is the
object located
at 3s?
At what point
is the object at
7m?
What is
happening to the
object between
6-11s ?
What is happening
between 11-17s ?
• Velocity- the speed of an object in a
specific direction; it is a vector quantity
because it describes magnitude (how fast)
and direction
• Speed- is simply how fast something is
moving; It is a scalar quantity because
there is no direction associated with it
Average Velocity
Velocity is defined as: “The RATE at which
DISPLACEMENT changes”.
d
d
d
If you are given a Displacement
vs. Time graph, to find the velocity of an
object during specific time
intervals simply find the slope.
Slope
d
d
d
Because velocity
is a vector
quantity the
direction is
usually described
as being in a
positive or
negative
(backwards)
direction
What is the
average velocity
of the object
between 6-11s?
0 m/s object is
stopped
What is the
average velocity
of the object
between 0-6s?
1.7 m/s in a
positive direction
What is the
average velocity of
the object between
15-17s?
-1.5 m/s in a
negative direction
Average Speed - the average speed of an
object does not indicate direction therefore is
equal to the absolute value of average
velocity
Instantaneous velocity – the speed and
direction of an object at a specific time.
Instantaneous speed – the speed of an object
at a specific time
Equations are often more useful than
displacement-time graphs; If an
object is moving at a constant
velocity its graph will be a straight
line.
y=mx + b
d= vt + di
d position/displacement of object
v average velocity
t time
d initial position