1
COURSE TITLE
PHY 2048.981 General Physics I (w\calculus)
INSTRUCTOR
Zhimin Shi
MEETING TIMES
Section 981
Phone: 813-974-3611 E-mail: [email protected]
TR 6:30pm 7:45pm
ISA 1051
IMPORTANT NOTES
This course will use the associated Canvas web site to post
S E C T I O N 2 . 3 Acceleration
31
2.3 Acceleration
In the last example, we worked with a situation in which the velocity of a particle
changes while the particle is moving. This is an extremely common occurrence. (How
constant is your velocity as you ri
C H A P T E R 2 Motion in One Dimension
32
L
PITFALL PREVENTION
2.4 Negative
Acceleration
Keep in mind that negative acceleration does not necessarily mean that
an object is slowing down. If the acceleration is negative, and the velocity is negative, the
S E C T I O N 2 . 3 Acceleration
33
Quick Quiz 2.3
Make a velocitytime graph for the car in Figure 2.1a. The
speed limit posted on the road sign is 30 km/h. True or false? The car exceeds the
speed limit at some time within the interval.
Conceptual Exampl
S E C T I O N 2 . 2 Instantaneous Velocity and Speed
60
x(m)
60
40
20
0
40
20
40
60
29
0
10
20
30
(a)
40
50
t(s)
(b)
Active Figure 2.3 (a) Graph representing the motion of the car in Figure 2.1. (b) An
enlargement of the upper-left-hand corner of the gr
S E C T I O N 2 . 1 Position, Velocity, and Speed
25
Table 2.1
60
50
Position of the Car at
Various Times
IT
LIM
/h
30 km
40
30
20
10
0
10
Position
20
30
40
50
60
x(m)
60
50
40
30
20
x
10
0
10
20
30
20
40
t(s)
0
50
60
x(m)
Active Figure 2.1 (a) A car move
C H A P T E R 2 Motion in One Dimension
28
Example 2.1 Calculating the Average Velocity and Speed
Find the displacement, average velocity, and average speed
of the car in Figure 2.1a between positions and .
Solution From the positiontime graph given in Fi
S E C T I O N 2 . 1 Position, Velocity, and Speed
27
particles displacement x divided by the time interval t during which that
displacement occurs:
vx
x
t
(2.2)
Average velocity
where the subscript x indicates motion along the x axis. From this denition
Problems
17
nal answer is the same as the number of signicant gures in the quantity having the
lowest number of signicant gures. The same rule applies to division. When numbers
are added or subtracted, the number of decimal places in the result should equ
30
C H A P T E R 2 Motion in One Dimension
Conceptual Example 2.2 The Velocity of Different Objects
Consider the following one-dimensional motions: (A) A ball
thrown directly upward rises to a highest point and falls
back into the throwers hand. (B) A rac
S E C T I O N 2 . 4 Motion Diagrams
35
v
(a)
v
(b)
a
v
(c)
a
Active Figure 2.9 (a) Motion diagram for a car moving at constant velocity (zero
acceleration). (b) Motion diagram for a car whose constant acceleration is in the
direction of its velocity. The
S E C T I O N 2 . 5 One-Dimensional Motion with Constant Acceleration
The slope of the tangent line to this curve at t 0 equals the initial velocity vxi ,
and the slope of the tangent line at any later time t equals the velocity vxf at that
time.
Finally,
1
COURSE TITLE
PHY 2048.981 General Physics I (w\calculus)
INSTRUCTOR
Zhimin Shi
MEETING TIMES
Section 981
Phone: 813-974-3611 E-mail: [email protected]
TR 6:30pm 7:45pm
ISA 1051
IMPORTANT NOTES
This course will use the associated Canvas web site to post
42
C H A P T E R 2 Motion in One Dimension
Conceptual Example 2.11
Follow the Bouncing Ball
A tennis ball is dropped from shoulder height (about 1.5 m)
and bounces three times before it is caught. Sketch graphs
of its position, velocity, and acceleration
C H A P T E R 2 Motion in One Dimension
36
2.5 One-Dimensional Motion with Constant
Acceleration
x
Slope = vx f
xi
Slope = vxi
t
t
0
(a)
If the acceleration of a particle varies in time, its motion can be complex and difcult to
analyze. However, a very co
S E C T I O N 2 . 6 Freely Falling Objects
are released. Any freely falling object experiences an acceleration directed
downward, regardless of its initial motion.
We shall denote the magnitude of the free-fall acceleration by the symbol g. The value of
g
C H A P T E R 2 Motion in One Dimension
40
The trooper overtakes the car at the instant her position
matches that of the car, which is position :
x trooper x car
1
(3.00
2
time will be less than 31 s. Mathematically, let us cast the nal quadratic equation
34
C H A P T E R 2 Motion in One Dimension
Solution The velocity at any time t is vxi (40 5t 2 ) m/s
and the velocity at any later time t t is
vx(m/s)
40
vxf 40 5(t t)2 40 5t 2 10t t 5(t)2
30
Therefore, the change in velocity over the time interval t is
v
S E C T I O N 2 . 5 One-Dimensional Motion with Constant Acceleration
Example 2.7 Carrier Landing
A jet lands on an aircraft carrier at 140 mi/h ( 63 m/s).
(A) What is its acceleration (assumed constant) if it stops in
2.0 s due to an arresting cable that
38
C H A P T E R 2 Motion in One Dimension
Table 2.2
Kinematic Equations for Motion of a Particle Under Constant Acceleration
Equation
Information Given by Equation
vxf vxi a xt
x f x i 1(vxi vxf )t
2
x f x i vxi t 1ax t 2
2
v xf 2 v xi 2 2a x(x f x i)
Ve
C H A P T E R 2 Motion in One Dimension
From this denition we see that x is positive if xf is greater than xi and negative if xf is
less than xi.
It is very important to recognize the difference between displacement and distance
traveled. Distance is the
As a rst step in studying classical mechanics, we describe motion in terms of space
and time while ignoring the agents that caused that motion. This portion of classical
mechanics is called kinematics. (The word kinematics has the same root as cinema. Can
C H A P T E R 1 Physics and Measurement
12
Example 1.2 Analysis of an Equation
Show that the expression v at is dimensionally correct,
where v represents speed, a acceleration, and t an instant of
time.
The same table gives us L/T2 for the dimensions of a
S E C T I O N 1 . 4 Dimensional Analysis
Table 1.6
Units of Area, Volume, Velocity, Speed, and Acceleration
System
Area
(L2)
Volume
(L3)
Speed
(L/T)
Acceleration
(L/T 2)
SI
U.S. customary
m2
ft2
m3
ft3
m/s
ft/s
m/s2
ft/s2
dimensions can be treated as alge
C H A P T E R 1 Physics and Measurement
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The atomic mass of lead is 207 u and that of aluminum is 27.0 u. However, the ratio of
atomic masses, 207 u/27.0 u 7.67, does not correspond to the ratio of densities,
(11.3 103 kg/m3)/(2.70 103 kg/m3) 4.19. This
S E C T I O N 1 . 3 Density and Atomic Mass
is to act as a glue that holds the nucleus together. If neutrons were not present in the
nucleus, the repulsive force between the positively charged particles would cause the
nucleus to come apart.
But is this w
S E C T I O N 1 . 2 Matter and Model Building
Table 1.4
Prexes for Powers of Ten
Power
Prex
Abbreviation
1024
1021
1018
1015
1012
109
106
103
102
101
103
106
109
1012
1015
1018
1021
1024
yocto
zepto
atto
femto
pico
nano
micro
milli
centi
deci
kilo
mega
gi
C H A P T E R 1 Physics and Measurement
(Courtesy of National Institute of Standards and Technology, U.S. Department of Commerce)
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(a)
(b)
Figure 1.1 (a) The National Standard Kilogram No. 20, an accurate copy of the
International Standard Kilogram kept
S E C T I O N 1 . 1 Standards of Length, Mass, and Time
Table 1.1
L
Approximate Values of Some Measured Lengths
Length (m)
Distance from the Earth to the most remote known quasar
Distance from the Earth to the most remote normal galaxies
Distance from the
4
C H A P T E R 1 Physics and Measurement
(4) several remarkable results in genetic engineering. The impacts of such developments and discoveries on our society have indeed been great, and it is very likely that
future discoveries and developments will be