Physics 204A Class Notes
21
Section 2  Motion In One Dimension
Section Outline
1. The Definition of Position
2. The Definition of Displacement
3. The Definition of Average Velocity
4. The Definitions of Instantaneous Velocity and Speed
5. The Definitions of Average Acceleration and Instantaneous Acceleration
6. The Calculus of Motion
7. The Special Case of Constant Acceleration
8. Freely Falling Bodies
9. Nonconstant Acceleration
Let’s start to answer the question, “What do objects do?”
Whether the object is an atom, a baseball, or a
star, they all move.
So, we need to be able to thoroughly describe motion. We will not worry about the
cause of the motion – that will come later.
The description of motion is called “Kinematics.”
We’ll
begin by very carefully defining the words and ideas we’ll use.
1. The Definition of Position
The first step is to describe the location of the object is to know where it is.
The Definition of Position:
The location of an object with respect to a coordinate system.
The location of an object is meaningless unless it is referenced to something.
In physics, that something
is called a coordinate system or frame of reference.
You can choose any coordinate system that you
would like, however, you must always indicate which one you have chosen. We’ll discover that there
are distinct advantages to using certain coordinate systems as we go further.
For now, we’ll usually just
the describe the position as the location along the xaxis as shown above.
Rewritten mathematically,
The Definition of Position: x
2. The Definition of Displacement
Physics wouldn’t be very interesting if objects stayed in one place.
So the next thing we need to define
is changes in location.
The Definition of Displacement: A change in position.
Rewritten mathematically,
The Definition of Displacement:
"
x
#
x
f
$
x
i
x
y
x
x
y
x
f
x
i
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Physics 204A Class Notes
22
Example 2.1: At the right is a graph of my last trip to Los Angeles.
The origin is at Chico.
Find
(a)my position at t=2h, (b) my position at t=8h, (c) my displacement during these 6h and (d)my
total displacement.
In
this
example,
the
coordinate
system has been chosen for us.
The
origin is at Chico and the xaxis
points toward Los Angeles.
(a)We can get position values by
reading the graph, x
i
= 110mi.
(b)Again, reading the graph, x
f
=
375mi.
(c)Using the definition of
displacement,
!
x
"
x
f
#
x
i
=
375
#
110
$
∆
x = 265mi.
(d)Estimating from the graph, using
the definition of displacement,
"
x
#
x
f
$
x
i
=
495
$
0
%
∆
x
ot
= 495mi.
3. The Definition of Average Velocity
The next step is to describe how quickly the location is changing (How fast is it going?)
The Definition of Average Velocity: The average rate of displacement.
Mathematically,
The Definition of Average Velocity:
v
!
"
x
"
t
=
x
f
#
x
i
t
f
#
t
i
Example 2.2: Find my average velocity (a)during the interval from t = 2h to t = 8h and (b)for
the entire trip.
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 Fall '09
 Kagan
 Physics, Acceleration, Kinematic equation, Velocity, Physics 204A Class, 204A Class Notes

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