Kinematics
The study of how objects move
Where are You?
We must start with a
question
Position
Reference Point:
Zero location in a coordinate
system or frame.
Frame of Reference:
Coordinate system used to define
motion.
Position:
Separation between an object and a
reference point. It needs a distance and direction.
i.e. 3.0 meters to the right.
To find where you are you need the following:
You are Here
You are Here
You are Here
You are Here
You are Here
You are Here
You are Here
You are Here
Distance vs. Displacement
Distance is simply the total path length
traversed in moving from one location
to another
Distance is a SCALAR quantity. A measurement
with only magnitude, or size.
50 m
Distance vs. Displacement
Displacement is the straight

line distance between
two points, along with the direction from the
starting point to the final position.
Displacement is a VECTOR quantity. A
measurement with magnitude, or size and
a direction
10 m East
Difference between
Distance and
Displacement
Walking to
Physics Lab
Distance = 8 m
Displacement = 8m right
Right

Positive
Left

Negative
Direction Convention :
Displacement =+8m
Speed
Speed
Time
Distance
Speed is the rate at which distance is traveled.
=10 m/s
20 m
2 sec
Speed
m
20
2
sec
Speed is a scalar
quanity
Average speed
is the distance
d
traveled, the actual path, divided
by the total time
t
elapsed in traveling that distance.
Average Sp
eed
Distance T
raveled
Total Time
Instantaneous Speed
is how fast an object is moving at a
particular instant of time.
Average vs.
Instantaneous Speed
Velocity
V
x
t
x
x
t
t
o
o
x
o
t
o
Velocity
tells how fast something is moving
and
in what
direction. Velocity is a vector quantity.
Average Velocity
is the displacement divided by the total
travel time
=initial position, commonly
zero
= initial time, commonly zero
V
x
t
When x
o
and t
o
are zero
A jogger jogs from one end to the other of a straight 300 meter track
(from point A to point B) in 2.50 min and then turns around and
jogs 100 m back toward the starting point (to point C) in another
1.00 min. What are the jogger’s average speeds and velocities in
going
A)
From A to B
B) From A to C after turning around
Speed
and
Velocity
Problem
avg speed
d
t
m
s
m
s
300
150
2
00
.
v
x
t
m
s
B
B
m
s
300
150
2
00
.
A)
v
x
x
t
t
m
m
s
s
c
B
C
B
C
m
s
300
100
150
60
0
0
952
(
)
.
.
Given:
x
B
= 300m

0m = +300m (from A to B)
x
C
= 200m
–
300m =

100m (from B to C)
t
B
= 2.50 min = 150 s
t
C
= 1.00 min = 60.0 s
B)
Average speed and velocity from A to B
Average speed and velocity from A to C
avg speed
d
t
m
m
s
s
m
s
300
100
150
60
0
1
90
.
.
Two Components
of Velocity
Graphical look
at Motion
Acceleration
Position is the separation between an object
and a reference point.
Displacement is a change in position
Velocity is the time rate change of displacement
Acceleration is the time rate change of velocity
All four are vector quantities
Represented by a magnitude and direction
K
i
n
e
m
a
t
i
c
E
q
u
a
t
i
o
n
s
v
d
t
d
d
t
t
2
1
2
1
d
d
t
2
1
a
v
t
v
v
t
t
2
1
2
1
v
v
t
2
1
v
v
at
2
1
acceleration
velocity
v
d
t
v
v
v
1
2
2
d
t
v
v
1
2
2
With a constant acceleration
Total Displacement and total time
Average Velocity
d
v
v
t
1
2
1
2
(
)
d
v
v
t
1
2
1
2
(
)
v
v
at
2
1
v
at
1
d
v
v
at
t
1
2
1
1
(
(
))
d
v
t
at
1
2
1
1
2
2
2
(
)
d
v
t
at
1
1
2
2
d
v
v
t
1
2
1
2
(
)
v
v
ad
2
2
1
2
2
d
v
v
a
2
2
1
2
2
d
v
v
v
v
a
1
2
2
1
2
t
v
v
a
2
1
d
v
t
v
v
at
2
1
v
v
1
2
2
v
v
v
1
2
2
v
v
a
2
1
K
i
n
e
m
a
t
i
c
E
q
u
a
t
i
o
n
s
v
d
t
v
v
at
2
1
a
v
t
d
v
t
at
1
1
2
2
v
v
ad
2
2
1
2
2
Problem:
Ally the Alligator takes off from an airfield.
She starts from rest and obtains a velocity of
36 m/s at take off in 20.0 seconds.
What is her acceleration down the runway?
How far did she go down the runway?
a
v
t
v
v
t
2
1
36
0
20
m
s
m
s
sec
1
8
2
.
m
s
1
8
2
.
m
s
d
v
v
t
1
2
1
2
(
)
d
m
s
m
s
1
2
0
36
20
0
(
)
.
sec
d
m
360
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