Raymond A. Serway
John W. Jewett
Chapter 2
Motion in One Dimension

The Study of Motion
•
Kinematics
describes motion while ignoring
the agents that caused the motion
•
For now, we will consider motion in one
dimension
•
Along a straight line
•
We will use the particle model
•
A particle is a point-like object, has mass but
infinitesimal size

2.1 Average Velocity
•
Average
speed
is defined as
•
Speed is not a vector, so has no direction
•
Average velocity
is a vector quantity

2.1 Average Velocity
•
The motion of a particle can be specified if
its position is known at all times
•
Consider the car moving back and forth
along the
x
axis
•
The figure is a
pictorial
representation of the
motion
•
Imagine we take data
on the position of the
car every 10 s

2.1 Average Velocity
•
The
graphical
representation
of the
motion is a
position-time
graph
•
The smooth curve is
a guess as to what
happened between
the data points

2.1 Average Velocity
•
The
tabular
representation
of the
motion is shown
here
•
The data are entries
for position at each
time

2.1 Average Velocity
•
Average velocity
:
defined as ratio of
displacement
x
to time interval
t
•
Subscript
x
indicates motion along
x
axis
•
Dimensions: m/s (SI)
•
x
can be positive or negative

2.1 Average Velocity
•
Average velocity can be interpreted geometrically
•
A straight line can be drawn between any two points on
curve
•
Line forms the hypotenuse of right triangle of height
x
and base
t
•
Slope of hypotenuse is ratio
x
/
t
•
Average velocity during time
interval
t
is slope of the line
joining initial and final points
on the position-time graph

2.1 Average Velocity
•
The displacement of a particle during the time
interval
t
i
to
t
f
is equal to the area under the
curve between the initial and final points on a
velocity-time curve

Example 2.1 Calculating the Average
Velocity and Speed
Find the displacement, average velocity, and
average speed of the car between positions A
and F.
•
Find the displacement of the car:
•
Find the car’s average velocity:
•
Find the car’s average speed:

Example 2.2 Motion of a Jogger
A jogger runs in a straight line, with an average
velocity of magnitude 5.00 m/s for 4.00 min and
then with an average velocity of magnitude
4.00 m/s for 3.00 min.

Example 2.2 Motion of a Jogger
(A)
What is the magnitude of the final
displacement from her initial position?
•
Find the displacement for each portion:

Example 2.2 Motion of a Jogger
(B)
What is the magnitude of her average
velocity during this entire time interval of 7.00
min?
•
Find the average velocity for the entire time
interval:

2.2 Instantaneous Velocity
•
Instantaneous velocity
is the limit of the
average velocity as the time interval
becomes infinitesimally short
•
or as the time interval approaches zero
•
The instantaneous velocity indicates what is
happening at every point of time

2.2 Instantaneous Velocity
•
The instantaneous velocity is the slope of the
line tangent to the
x
vs.
t
curve
•
the green line in the figure
•
The blue lines show that as
t
gets smaller,
they approach the green line

2.2 Instantaneous Velocity

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