Kinematics
Motion in 1-Dimension
Lana Sheridan
De Anza College
Jan 13, 2016
Last time
• vector operations
• how to solve problems
Overview
• 1-D kinematics
• quantities of motion
• graphs of kinematic quantities vs time
Kinematics in 1-dimension
We begin by studying motion along a single line.
This will encompass situations like
• cars traveling along straight roads
• objects falling straight down under gravity
Distance vs Displacement
How far are two points from one another?
Distance is the length of a path that connects the two points.
Displacement is the length together with the direction of a
straight line that connects the starting position to the final
position.
Displacement is a vector.
Position
Quantities
position
displacement
distance
x
∆x = xf − xi
d
Position and displacement are vector quantities.
Position and displacement can be positive or negative
numbers.
Distance is a scalar so it is always a positive number.
Position
Quantities
position
displacement
distance
x
∆x = xf − xi
d
Position and displacement are vector quantities.
Position and displacement can be positive or negative
numbers.
Distance is a scalar so it is always a positive number.
Position
Quantities
position
displacement
distance
x
∆x = xf − xi
d
Position and displacement are vector quantities.
Position and displacement can be positive or negative
numbers.
Distance is a scalar so it is always a positive number.
Units: meters, m
Position
t (s)
x (m)
point. A graphical representation of thi
!
0
30
Such a plot isExample
called a position–time graph.
Position,
Displacement,
Distance
"
10
52
Notice the alternative representations o
%
20
38
motion of the car. Figure 2.1a is a pictor
$ The starting30position of 0
the cargraphical
is xi = 30
m i, the finalTable
position
representation.
2.1 isis a tabu
& xf = 50 m i.
40
237
Using an alternative representation is oft
#
50
253
the situation in a given problem. The u
The distance the car travels is d = 50 m − 30 m = 20 m.
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
0
10
20
30
"
40
50
−−−−−→
∆x
#
&
$
%
The displacement of the car is ∆x = xf − xi = 20 m i.
!60 !50 !40 !30 !20 !10
0
10
20
30
40
50
60
60
x (m)
40
!
20
60
x (m)
0
!20
Position, Displacement, Distance Example
The starting position of the car is xi = 30The
m car
i, the
final
moves
to position is
xf = −60 m i.
the right between
positions ! and ".
The distance the car travels is d = 130 m.
!
"
!60 !50 !40 !30 !20 !10
0
10
20
30
←−−−−−−−−−−−−−−−−−−−−−−−−−
∆x
#
&
$
!60 !50 !40 !30 !20 !10
0
10
20
30
The displacement of theThe
carcaris moves to
the left between
∆xpositions
= x%
x i #.
f −and
a
= (−60i) − 30i m
= −90 m i
40
50
60
x (m)
40
!
20
%
40
x
60
50
60
x (m)
0
!20
!40
!60
b
Speed
We need a measure how fast objects move.
speed =
distance
time
If an object goes 100 m in 1 second, its speed is 100 m/s.
Speed
Speed can change with time.
For example, driving. Sometimes you are on the highway,
sometime you wait at a stoplight.
Instantaneous speed is an object’s speed at any given moment in
time.
Speed
Speed can change with time.
For example, driving. Sometimes you are on the highway,
sometime you wait at a stoplight.
Instantaneous speed is an object’s speed at any given moment in
time.
Average speed is the average of the object’s speed over a period
of time:
average speed =
total distance traveled
time interval
Velocity
Driving East at 65 mph is not the same as driving West at 65 mph.
Velocity
Driving East at 65 mph is not the same as driving West at 65 mph.
There is a quantity that combines the speed and the direction of
motion.
This is the velocity.
Velocity
Driving East at 65 mph is not the same as driving West at 65 mph.
There is a quantity that combines the speed and the direction of
motion.
This is the velocity.
Velocity is a vector quantity. Speed is a scalar quantity.
Velocity
Driving East at 65 mph is not the same as driving West at 65 mph.
There is a quantity that combines the speed and the direction of
motion.
This is the velocity.
Velocity is a vector quantity. Speed is a scalar quantity.
If a car drives in a circle, without speeding up or slowing down, is
its speed constant?
Velocity
Driving East at 65 mph is not the same as driving West at 65 mph.
There is a quantity that combines the speed and the direction of
motion.
This is the velocity.
Velocity is a vector quantity. Speed is a scalar quantity.
If a car drives in a circle, without speeding up or slowing down, is
its speed constant?
Is its velocity constant?
Velocity
How position changes with time.
Quantities
velocity
v
average velocity
vavg =
instantaneous speed
v or |v|
average speed
d
∆t
∆x
∆t
Velocity
How position changes with time.
Quantities
velocity
v
average velocity
vavg =
instantaneous speed
v or |v|
average speed
Can velocity be negative?
d
∆t
∆x
∆t
Velocity
How position changes with time.
Quantities
velocity
v
average velocity
vavg =
instantaneous speed
v or |v|
average speed
Can velocity be negative?
Can speed be negative?
d
∆t
∆x
∆t
Velocity
How position changes with time.
Quantities
velocity
v
average velocity
vavg =
instantaneous speed
v or |v|
average speed
∆x
∆t
d
∆t
Can velocity be negative?
Can speed be negative?
Units: meters per second, m/s
point. A graphical representation of thi
!
0
Such aSpeed
plot is called
a position–time graph.
Average
Velocity
vs30
Average
Example
"
10
52
Notice the alternative representations o
% The displacement
20
of the38car is motion
∆x = 20ofmthe
i. car. Figure 2.1a is a pictor
$
30
0
graphical
representation.
Table 2.1 is a tabu
& The distance
40the car travels
237 is d = 20 m.
Using an alternative representation is oft
# The time for
50the car to
253
move this far is 10 seconds.
the situation in a given problem. The u
What is the average velocity of the car? What is the average speed
of the car?
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
!60 !50 !40 !30 !20 !10
0
10
20
$
0
10
20
30
"
40
50
−−−−−→
∆x
%
30
40
50
60
60
x (m)
40
!
20
60
x (m)
0
!20
point. A graphical representation of thi
!
0
Such aSpeed
plot is called
a position–time graph.
Average
Velocity
vs30
Average
Example
"
10
52
Notice the alternative representations o
% The displacement
20
of the38car is motion
∆x = 20ofmthe
i. car. Figure 2.1a is a pictor
$
30
0
graphical
representation.
Table 2.1 is a tabu
& The distance
40the car travels
237 is d = 20 m.
Using an alternative representation is oft
# The time for
50the car to
253
move this far is 10 seconds.
the situation in a given problem. The u
What is the average velocity of the car? What is the average speed
of the car?
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
average velocity vavg =
∆x
∆t
0
20
$
= 2 m/s i
d
= 2 m/s
∆t !20
!60 !50 !40 !30
!10 0
average speed =
10
30
"
40
−−−−−→
∆x
%
(same in this case)
10
20
50
30
40
50
60
60
x (m)
40
!
20
60
x (m)
0
!20
50
#
253
the situation in a given problem. The u
Average Velocity vs Average Speed Example
The displacement of the car is −90 m i.
The distance the car travels is d = 130 m.The car moves to
the right between
The time for the car to move A→E is 50 positions
seconds.
! and ".
Average velocity? Average speed?
!60 !50 !40 !30 !20 !10
0
!
10
20
30
←−−−−−−−−−−−−−−−−−−−−−−−−−
∆x
#
&
$
!60 !50 !40 !30 !20 !10
a
0
10
20
30
x
60
"
40
50
60
x (m)
20
%
40
40
!
50
60
x (m)
0
!20
The car moves to
the left between
!40
positions % and #.
!60
b
50
#
253
the situation in a given problem. The u
Average Velocity vs Average Speed Example
The displacement of the car is −90 m i.
The distance the car travels is d = 130 m.The car moves to
the right between
The time for the car to move A→E is 50 positions
seconds.
! and ".
Average velocity? Average speed?
!60 !50 !40 !30 !20 !10
0
!
10
20
30
←−−−−−−−−−−−−−−−−−−−−−−−−−
∆x
#
&
$
!60 !50 !40 !30 !20 !10
0
10
20
30
40
40
The car moves to
average speed =
a
= 2.6 m/s
50
60
x (m)
Not the same!
40
!
20
%
∆x left between
average velocity vavg = the
∆t = −1.8 m/s i
positions % and #.
d
∆t
x
60
"
50
60
x (m)
0
!20
!40
!60
b
Question
Quick Quiz 2.11 Under which of the following conditions is the
magnitude of the average velocity of a particle moving in one
dimension smaller than the average speed over some time interval?
A A particle moves in the +x direction without reversing.
B A particle moves in the −x direction without reversing.
C A particle moves in the +x direction and then reverses the
direction of its motion.
D There are no conditions for which this is true.
(http://www.quizsocket.com)
1
Serway & Jewett, page 24.
Question
Quick Quiz 2.11 Under which of the following conditions is the
magnitude of the average velocity of a particle moving in one
dimension smaller than the average speed over some time interval?
A A particle moves in the +x direction without reversing.
B A particle moves in the −x direction without reversing.
C A particle moves in the +x direction and then reverses the
direction of its motion.
←
D There are no conditions for which this is true.
(http://www.quizsocket.com)
1
Serway & Jewett, page 24.
y
rankings, remember that zero is greater than a negative
Conceptual
value. IfQuestion
two values are equal, show that they are equal
in your ranking.)
Conceptual Questions
c
1. denotes answer available in Student So
1. If the average velocity of an object is zero in some time
interval, what can you say about the displacement of
the object for that interval?
2. Try the following experiment away from traffic where
you can do it safely. With the car you are driving moving slowly on a straight, level road, shift the transmission into neutral and let the car coast. At the moment
the car comes to a complete stop, step hard on the
brake and notice what you feel. Now repeat the same
experiment on a fairly gentle, uphill slope. Explain the
difference in what a person riding in the car feels in
1 the two cases. (Brian Popp suggested the idea for this
Serway & Jewett, page 50.
6. Y
g
w
a
w
e
7. (
b
i
z
8. (
b
Acceleration
Speed and velocity can change with time.
Acceleration is the rate of change of velocity with time.
acceleration =
change in velocity
time interval
Acceleration
Speed and velocity can change with time.
Acceleration is the rate of change of velocity with time.
acceleration =
change in velocity
time interval
If an object is moving with constant speed in a circular path, is it
accelerating?
Acceleration
Quantities
acceleration
average acceleration
Acceleration is also a vector quantity.
a
aavg =
∆v
∆t
Acceleration
Quantities
acceleration
average acceleration
a
aavg =
∆v
∆t
Acceleration is also a vector quantity.
If the acceleration vector is pointed in the same direction as the
velocity vector (ie. both are positive or both negative), the
particle’s speed is increasing.
Acceleration
Quantities
acceleration
average acceleration
a
aavg =
∆v
∆t
Acceleration is also a vector quantity.
If the acceleration vector is pointed in the same direction as the
velocity vector (ie. both are positive or both negative), the
particle’s speed is increasing.
If the acceleration vector is pointed in the opposite direction as
the velocity vector (ie. one is positive the other is negative), the
particle’s speed is decreasing. (It is “decelerating”.)
Graphing Kinematic Quantities
One very convenient way of representing motion is with graphs
that show the variation of these kinematic quantities with time.
Time is written along the horizontal axis – we are representing
time passing with a direction in space (the horizontal direction).
Table 2.1 Position of
the Car at Various Times
origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than
50 m to the left of x 5 0 when we stop recording information after our sixth data
point. A graphical representation of this information is presented in Figure 2.1b.
Such a plot is called a position–time graph.
Notice the alternative representations of information that we have used for the
motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a
graphical representation. Table 2.1 is a tabular representation of the same information.
Using an alternative representation is often an excellent strategy for understanding
the situation in a given problem. The ultimate goal in many problems is a math-
Position
vs. 30Time Graphs
!
0
Position
t (s)
x (m)
"
%
$
&
#
10
20
30
40
50
52
38
0
237
253
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
0
10
20
30
$
!60 !50 !40 !30 !20 !10
0
x (m)
60
"
40
50
60
x (m)
10
20
30
40
The car moves to
the left between
positions % and #.
"x
!
50
60
x (m)
%
"t
20
%
"
40
$
0
!20
&
!40
!60
#
0
10
20
30
40
50
t (s)
b
a
Figure 2.1
A car moves back and forth along a straight line. Because we are interested only in the
car’s translational motion, we can model it as a particle. Several representations of the information
about the motion of the car can be used. Table 2.1 is a tabular representation of the information.
(a) A pictorial representation of the motion of the car. (b) A graphical representation (position–time
graph) of the motion of the car.
1
Figures from Serway & Jewett
Table 2.1 Position of
the Car at Various Times
origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than
50 m to the left of x 5 0 when we stop recording information after our sixth data
point. A graphical representation of this information is presented in Figure 2.1b.
Such a plot is called a position–time graph.
Notice the alternative representations of information that we have used for the
motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a
graphical representation. Table 2.1 is a tabular representation of the same information.
Using an alternative representation is often an excellent strategy for understanding
the situation in a given problem. The ultimate goal in many problems is a math-
Position
vs. 30Time Graphs
!
0
Position
t (s)
x (m)
"
%
$
&
#
10
20
30
40
50
52
38
0
237
253
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
0
10
20
30
$
!60 !50 !40 !30 !20 !10
0
x (m)
60
"
40
50
60
x (m)
10
20
30
40
The car moves to
the left between
positions % and #.
"x
!
50
60
x (m)
%
"t
20
%
"
40
$
0
!20
&
!40
!60
#
0
10
20
30
40
50
t (s)
b
a
Figure 2.1
A car moves back and forth along a straight line. Because we are interested only in the
car’s translational motion, we can model it as a particle. Several representations of the information
about the motion of the car can be used. Table 2.1 is a tabular representation of the information.
(a) A pictorial representation of the motion of the car. (b) A graphical representation (position–time
graph) of the motion of the car.
1
Figures from Serway & Jewett
Table 2.1 Position of
the Car at Various Times
origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than
50 m to the left of x 5 0 when we stop recording information after our sixth data
point. A graphical representation of this information is presented in Figure 2.1b.
Such a plot is called a position–time graph.
Notice the alternative representations of information that we have used for the
motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a
graphical representation. Table 2.1 is a tabular representation of the same information.
Using an alternative representation is often an excellent strategy for understanding
the situation in a given problem. The ultimate goal in many problems is a math-
Position
vs. 30Time Graphs
!
0
Position
t (s)
x (m)
"
%
$
&
#
10
20
30
40
50
52
38
0
237
253
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
0
10
20
30
$
!60 !50 !40 !30 !20 !10
0
x (m)
60
"
40
50
60
x (m)
10
20
30
40
The car moves to
the left between
positions % and #.
"x
!
50
60
x (m)
%
"t
20
%
"
40
$
0
!20
&
!40
!60
#
0
10
20
30
40
50
t (s)
b
a
Figure 2.1
A car moves back and forth along a straight line. Because we are interested only in the
car’s translational motion, we can model it as a particle. Several representations of the information
about the motion of the car can be used. Table 2.1 is a tabular representation of the information.
(a) A pictorial representation of the motion of the car. (b) A graphical representation (position–time
graph) of the motion of the car.
1
Figures from Serway & Jewett
Table 2.1 Position of
the Car at Various Times
origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than
50 m to the left of x 5 0 when we stop recording information after our sixth data
point. A graphical representation of this information is presented in Figure 2.1b.
Such a plot is called a position–time graph.
Notice the alternative representations of information that we have used for the
motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a
graphical representation. Table 2.1 is a tabular representation of the same information.
Using an alternative representation is often an excellent strategy for understanding
the situation in a given problem. The ultimate goal in many problems is a math-
Position
vs. 30Time Graphs
!
0
Position
t (s)
x (m)
"
%
$
&
#
10
20
30
40
50
52
38
0
237
253
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
0
10
20
30
$
!60 !50 !40 !30 !20 !10
0
x (m)
60
"
40
50
60
x (m)
10
20
30
40
The car moves to
the left between
positions % and #.
"x
!
50
60
x (m)
%
"t
20
%
"
40
$
0
!20
&
!40
!60
#
0
10
20
30
40
50
t (s)
b
a
Figure 2.1
A car moves back and forth along a straight line. Because we are interested only in the
car’s translational motion, we can model it as a particle. Several representations of the information
about the motion of the car can be used. Table 2.1 is a tabular representation of the information.
(a) A pictorial representation of the motion of the car. (b) A graphical representation (position–time
graph) of the motion of the car.
1
Figures from Serway & Jewett
Table 2.1 Position of
the Car at Various Times
origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than
50 m to the left of x 5 0 when we stop recording information after our sixth data
point. A graphical representation of this information is presented in Figure 2.1b.
Such a plot is called a position–time graph.
Notice the alternative representations of information that we have used for the
motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a
graphical representation. Table 2.1 is a tabular representation of the same information.
Using an alternative representation is often an excellent strategy for understanding
the situation in a given problem. The ultimate goal in many problems is a math-
Position
vs. 30Time Graphs
!
0
Position
t (s)
x (m)
"
%
$
&
#
10
20
30
40
50
52
38
0
237
253
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
0
10
20
30
$
!60 !50 !40 !30 !20 !10
0
x (m)
60
"
40
50
60
x (m)
10
20
30
40
The car moves to
the left between
positions % and #.
"x
!
50
60
x (m)
%
"t
20
%
"
40
$
0
!20
&
!40
!60
#
0
10
20
30
40
50
t (s)
b
a
Figure 2.1
A car moves back and forth along a straight line. Because we are interested only in the
car’s translational motion, we can model it as a particle. Several representations of the information
about the motion of the car can be used. Table 2.1 is a tabular representation of the information.
(a) A pictorial representation of the motion of the car. (b) A graphical representation (position–time
graph) of the motion of the car.
1
Figures from Serway & Jewett
Table 2.1 Position of
the Car at Various Times
origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than
50 m to the left of x 5 0 when we stop recording information after our sixth data
point. A graphical representation of this information is presented in Figure 2.1b.
Such a plot is called a position–time graph.
Notice the alternative representations of information that we have used for the
motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a
graphical representation. Table 2.1 is a tabular representation of the same information.
Using an alternative representation is often an excellent strategy for understanding
the situation in a given problem. The ultimate goal in many problems is a math-
Position
vs. 30Time Graphs
!
0
Position
t (s)
x (m)
"
%
$
&
#
10
20
30
40
50
52
38
0
237
253
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
0
10
20
30
$
!60 !50 !40 !30 !20 !10
0
x (m)
60
"
40
50
60
x (m)
10
20
30
40
The car moves to
the left between
positions % and #.
"x
!
50
60
x (m)
%
"t
20
%
"
40
$
0
!20
&
!40
!60
#
0
10
20
30
40
50
t (s)
b
a
Figure 2.1
A car moves back and forth along a straight line. Because we are interested only in the
car’s translational motion, we can model it as a particle. Several representations of the information
about the motion of the car can be used. Table 2.1 is a tabular representation of the information.
(a) A pictorial representation of the motion of the car. (b) A graphical representation (position–time
graph) of the motion of the car.
1
Figures from Serway & Jewett
Table 2.1 Position of
the Car at Various Times
origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than
50 m to the left of x 5 0 when we stop recording information after our sixth data
point. A graphical representation of this information is presented in Figure 2.1b.
Such a plot is called a position–time graph.
Notice the alternative representations of information that we have used for the
motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a
graphical representation. Table 2.1 is a tabular representation of the same information.
Using an alternative representation is often an excellent strategy for understanding
the situation in a given problem. The ultimate goal in many problems is a math-
Position
vs. 30Time Graphs
!
0
Position
t (s)
x (m)
"
%
$
&
#
10
20
30
40
50
52
38
0
237
253
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
0
10
20
30
$
!60 !50 !40 !30 !20 !10
0
x (m)
60
"
40
50
60
x (m)
10
20
30
40
The car moves to
the left between
positions % and #.
"x
!
50
60
x (m)
%
"t
20
%
"
40
$
0
!20
&
!40
!60
#
0
10
20
30
40
50
t (s)
b
a
Figure 2.1
A car moves back and forth along a straight line. Because we are interested only in the
car’s translational motion, we can model it as a particle. Several representations of the information
about the motion of the car can be used. Table 2.1 is a tabular representation of the information.
(a) A pictorial representation of the motion of the car. (b) A graphical representation (position–time
graph) of the motion of the car.
1
Figures from Serway & Jewett
Position
t (s)
x (m)
!
"
%
$
&
#
0
10
20
30
40
50
30
52
38
0
237
253
point. A graphical representation of this information is presented in Figure 2.1b.
Such a plot is called a position–time graph.
Notice the alternative representations of information that we have used for the
motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a
graphical representation. Table 2.1 is a tabular representation of the same information.
Using an alternative representation is often an excellent strategy for understanding
the situation in a given problem. The ultimate goal in many problems is a math-
Position vs. Time Graphs
The car moves to
the right between
positions ! and ".
!
!60 !50 !40 !30 !20 !10
#
&
0
10
20
30
$
!60 !50 !40 !30 !20 !10
0
x (m)
60
"
40
50
60
x (m)
10
20
30
40
"x
!
50
The car moves to
the left between
positions % and #.
60
x (m)
%
"t
20
%
"
40
$
0
!20
&
!40
!60
#
0
10
20
30
40
50
t (s)
b
a
Figurein
2.1 the
A car moves back and forth along a straight line. Because we are interested only in the
The average velocity
interval A→B is the slope of the blue
car’s translational motion, we can model it as a particle. Several representations of the information
about the motion of the car can be used. Table 2.1 is∆x
a tabular representation of the information.
line connecting the(a) points
A and B. vavgof=
A pictorial representation of the motion
the car.
∆t(b) A graphical representation (position–time
graph) of the motion of the car.
1
Figures from Serway & Jewett
Average Velocity in Position vs. Time Graphs
Chapter 2 Motion in One Dimension
A→B: vavg = ∆x
∆t = 2 m/s i
x (m)
60
60
"
%
40
!
20
#
0
40
!20
$
!40
!60
a
A→E: vavg =
&
0
10
∆x
∆t
20
= −1.8 m/s i
Figure 2.3
30
40
t (s)
50
!
b
(a) Graph representing the motion of the car in F
Velocity in Position vs. Time Graphs
The (instantaneous) velocity is the rate of change of
displacement ⇒ the slope of a velocity-time graph.
hapter 2 Motion in One Dimension
Pos.-time graph for car
x (m)
60
zoomed in
60
"
%
40
!
"
20
#
0
40
!20
$
!40
!60
a
" " "
&
0
10
20
30
40
t (s)
50
!
The blue line between
positions ! and "
approaches the green
tangent line as point " is
moved closer to point !.
b
(a) Graph
motiongives
of the car
in Figure
2.1. (b)
enlargement
The Figure
green2.3line
is therepresenting
tangenttheline,
the
slope
of An
the
curve of
atthe
upper-left-hand corner of the graph.
t = 0.
ny graph of
∆x
e represents
represents the velocity of thevcar
point !. What we have done is determine the
= at lim
e in the
∆t→0
∆t words, the instantaneous velocity vx
on the vertiinstantaneous velocity at that moment. In other
.2
in the quan-
equals the limiting value of the ratio Dx/Dt as Dt approaches zero:1
Summary
• quantities of motion
• graphs
Homework Walker Physics:
• Ch 2, onward from page 47. Ques: 1, 3; Probs: 1, 3, 5, 7
• Ch 1, onward from page 14. Problem: 51 (and look at
Lecture 5 slides solution)