ASSIGNMENT #1
LETTER OF INTRODUCTION
Welcome to AP Physics!
We are going to spend a lot of time together next year, so it’s best if I get a head start on learning a bit about you. Also we
will use the Internet and the Web a lot next year for this course, so let’s get you used to communicating with me via email.
Your first digital assignment is to successfully send me an e-mail. Due: Fri., June 20, 2014
Draft an e-mail to me following these rules:
a. Use clearly written, full sentences. Do not abbreviate words like you are on Facebook with a friend. Use spell
check! This is a professional communication like you would have with a college professor, so let’s practice for
your rapidly nearing future!
b. Address it to me at: nadumas19@gmail.com
c. Make the Subject: “AP Physics: Introduction of <Insert Your Name Here>” (Do not include
the quote marks or the brackets, just the words)
d. Begin the e-mail with a formal salutation, like “Mrs. Dumas,” or “Dear Mrs. Dumas,”
e. Now introduce yourself (your name) and tell me a little bit about yourself, like:
f.
•
Contact information: Include your email address for blogging purposes and your cell number for text
messaging. (Tell me your preferred method of contact.)
•
What do you like to do (hobbies, sports, music, interests, etc.)?
•
Do you have a job?
•
Tell me a little bit about your family (Mom? Dad? Guardian? Siblings? Pets?) What do your parents do for a
living?
•
Was there anything that you liked about your earlier biology or other science classes?
•
What was the last book you read for fun?
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What are you looking forward to the most in AP Physics?
•
What are you most anxious about in AP Physics?
End the e-mail with a formal closing: “Cordially”, “Sincerely”, “Warm regards”, etc. and add your name as if
you signed a letter.
AP Physics
Informational Websites
Below you will find some very helpful website that I advise you to work on in your spare time. These sites are
interactive and will provide you with some tutorial support during the summer.
1. AP Physics
http://www.physicsclassroom.com
2. Dimensional Analysis
http://www.wfu.edu/~ylwong/chem/dimensionanalysis/example1.html
3. Newtonian Mechanics
http://dev.physicslab.org/Compilations/APReview/MechanicsI.aspx
http://dev.physicslab.org/Compilations/APReview/MechanicsII.aspx
http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/
4. Fluid Mechanics and Thermal Physics
http://dev.physicslab.org/Compilations/APReview/Fluids.aspx
http://dev.physicslab.org/Compilations/APReview/Thermodynamics.aspx
http://scienceworld.wolfram.com/physics/topics/GeneralFluidMechanics.html
5. Electricity and Magnetism
http://dev.physicslab.org/Compilations/APReview/Electrostatics.aspx
http://dev.physicslab.org/Compilations/APReview/DCCircuits.aspx
http://dev.physicslab.org/Compilations/APReview/Magnetism.aspx
http://ocw.mit.edu/courses/physics/8-02sc-physics-ii-electricity-and-magnetism-fall-2010/
6. Waves and Optics
http://dev.physicslab.org/Compilations/APReview/WaveSound.aspx
7. Atomic and Nuclear Physics
http://dev.physicslab.org/Compilations/APReview/Modern.aspx
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AP Physics
Scientific Notation, Significant Figures, and the
Factor-Label Method of Solving Problems
Scientific Notation
Scientific notation (Chang, p. 21) is a type of exponential notation in which only one digit is kept to the left
of the decimal point. Example: 8.4050 x 10-8.
Significant Figures
It is reasonable that a calculated result can be no more precise than the least precise piece of information
that went into the calculation. Thus it is common practice to write numbers in scientific notation with only the
last place containing any uncertainty. When we do this we are keeping only the “significant figures” (Chang,
pgs 23-24).

To determine the number of significant figures in a number, you read the number from left to right and
count all digits starting with the first non-zero digit. Do not count the exponential part.
Thus the number 0.002050 contains 4 significant figures and is written in scientific notation as 2.050 x 10-3. The
trailing zeros in a non-decimal number such as 1200 may or may not be significant: the number may be written
as 1.2 x 102, 1.20 x 102 or 1.200 x 102 depending on whether it has 2, 3, or 4 significant figures.
Significant Figures in Derived Quantities
When doing calculations, you should use all the digits allowed by your calculator in all intermediate steps.
Then in the final step, round off your answer to the appropriate number of “significant figures” such that only
the last decimal place contains any uncertainty. You do this by following the rules:
•
When adding or subtracting, first express all numbers with the same exponent. Then the number of decimal
places in the answer should be equal to the number of decimal places in the number with the fewest decimal
places.
•
In multiplication or division, the number of significant figures in the answer should be the same as that in
the factor with the fewest significant figures.
When using these rules, assume that exact numbers have an infinite number of significant figures (or decimal
places). For example, there are exactly 12 inches in one foot.
Solving Problems Using Dimensional Analysis: The Factor-Label Method
Units may be used as a guide in solving problems. First decide what units you need for your answer. Then
determine what units you are given in the problem, and what conversion factors will take you from the given
units to the desired units. If the units cancel out properly, chances are that you are doing the right thing! The
basic set up is
 x new units 
? units desired = units given  
 ....
y units given 
Conversion factors are added until the new units are the same as the units desired. Each conversion factor has a
denominator equivalent to the numerator but in different units.
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AP Physics
Assignment # 2
1. Carry out the following mathematical operations and express your answer in scientific notation using the
proper number of significant figures.
(a) (4.28 x 10-4) + (3.564 x 10-2)
(b) (0.00950) x (8.501 x 107)  3.1425 x 10-11

________________________________________________________________________
2. Use the factor-label method to solve the following problem. Show your work, and give your answer in
scientific notation using the proper number of significant figures.
The calorie (1 cal = 4.184 J) is a unit of energy. The burning of a sample of gasoline produces 4.0 x 102 kJ of
heat. Convert this energy to calories. (103 J = 1 kJ.)
________________________________________________________________________
3. Use the factor-label method to solve the following problem. Show your work, and give your answer in
scientific notation using the proper number of significant figures.
The distance from the sun to the earth is 93 million miles. How many minutes does it take light from the sun to
reach earth?
Useful information: 1 km = 0.6214 mile, c = speed of light = 3.00 x 108 m/s)
pg. 4
AP Physics
Constant Velocity: Position-Time Graphs
MOTION IN A STRAIGHT LINE
In mechanics we are interested in trying to understand the motion of objects. In this chapter, the motion of
objects in 1 dimension will be discussed. Motion in 1 dimension is motion along a straight line.
2.1. Position
The position of an object along a straight line can be uniquely identified by its distance from a (user chosen)
origin. (see Figure 2.1). Note: the position is fully specified by 1 coordinate (that is why this a 1 dimensional
problem).
Figure 2.1. One-dimensional position.
Figure 2.2. x vs. t graphs for various velocities.
For a given problem, the origin can be chosen at whatever point is convenient. For example, the position of the
object at time t = 0 is often chosen as the origin. The position of the object will in general be a function of time:
x(t). Figure 2.2. shows the position as a function of time for an object at rest, and for objects moving to the left
and to the right.
The slope of the curve in the position versus time graph depends on the velocity of the object. See for example
Figure 2.3. After 10 seconds, the cheetah has covered a distance of 310 meter, the human 100 meter, and the pig
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AP Physics
50 meter. Obviously, the cheetah has the highest velocity. A similar conclusion is obtained when we consider
the time required to cover a fixed distance. The cheetah covers 300 meter in 10 s, the human in 30 s, and the pig
requires 60 s. It is clear that a steeper slope of the curve in the x vs. t graph corresponds to a higher velocity.
Figure 2.3. x vs. t graphs for various creatures.
2.2. Velocity
An object that changes its position has a non-zero velocity. The average velocity of an object during a
specified time interval is defined as:
If the object moves to the right, the average velocity is positive. An object moving to the left has a negative
average velocity. It is clear from the definition of the average velocity that depends only on the position of the
object at time t = t1 and at time t = t2. This is nicely illustrated in sample problem 2-1 and 2-2.
Sample Problem 2-1
You drive a beat-up pickup truck down a straight road for 5.2 mi at 43 mi/h, at which point you run out of fuel.
You walk 1.2 mi farther, to the nearest gas station, in 27 min (= 0.450 h). What is your average velocity from
the time you started your truck to the time that you arrived at the station ?
The pickup truck initially covers a distance of 5.2 miles with a velocity of 43 miles/hour. This takes 7.3
minutes. After the pickup truck runs out of gas, it takes you 27 minutes to walk to the nearest gas station which
is 1.2 miles down the road. When you arrive at the gas station, you have covered (5.2 + 1.2) = 6.4 miles, during
a period of (7.3 + 27) = 34.3 minutes. Your average velocity up to this point is:
Sample Problem 2-2
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AP Physics
Suppose you next carry the fuel back to the truck, making the round-trip in 35 min. What is your average
velocity for the full journey, from the start of your driving to you arrival back at the truck with the fuel ?
It takes you another 35 minutes to walk back to your car. When you reach your truck, you are again 5.2 miles
from the origin, and have been traveling for (34.4 + 35) = 69.4 minutes. At that point your average velocity is:
After this episode, you return back home. You cover the 5.2 miles again in 7.3 minutes (velocity equals 43
miles/hour). When you arrives home, you are 0 miles from your origin, and obviously your average velocity is:
The average velocity of the pickup truck which was left in the garage is also 0 miles/hour. Since the average
velocity of an object depends only on its initial and final location and time, and not on the motion of the object
in between, it is in general not a useful parameter. A more useful quantity is the instantaneous velocity of an
object at a given instant. The instantaneous velocity is the value that the average velocity approaches as the time
interval over which it is measured approaches zero:
For example: see sample problem 2-5.
The velocity of the object at t = 3.5 s can now be calculated:
2.3. Acceleration
The velocity of an object is defined in terms of the change of position of that object over time. A quantity used
to describe the change of the velocity of an object over time is the acceleration a. The average acceleration
over a time interval between t1 and t2 is defined as:
Note the similarity between the definition of the average velocity and the definition of the average acceleration.
The instantaneous acceleration a is defined as:
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AP Physics
From the definition of the acceleration, it is clear that the acceleration has the following units:
A positive acceleration is in general interpreted as meaning an increase in velocity. However, this is not correct.
From the definition of the acceleration, we can conclude that the acceleration is positive if
This is obviously true if the velocities are positive, and the velocity is increasing with time. However, it is also
true for negative velocities if the velocity becomes less negative over time.
2.4. Constant Acceleration
Objects falling under the influence of gravity are one example of objects moving with constant acceleration. A
constant acceleration means that the acceleration does not depend on time:
Integrating this equation, the velocity of the object can be obtained:
where v0 is the velocity of the object at time t = 0. From the velocity, the position of the object as function of
time can be calculated:
where x0 is the position of the object at time t = 0.
Note 1: verify these relations by integrating the formulas for the position and the velocity.
Note 2: the equations of motion are the basis for most problems (see sample problem 7).
Sample Problem 2-8
Spotting a police car, you brake a Porsche from 75 km/h to 45 km/h over a distance of 88m. a) What is the
acceleration, assumed to be constant ? b) What is the elapsed time ? c) If you continue to slow down with the
acceleration calculated in (a) above, how much time would elapse in bringing the car to rest from 75 km/h ? d)
In (c) above, what distance would be covered ? e) Suppose that, on a second trial with the acceleration
calculated in (a) above and a different initial velocity, you bring your car to rest after traversing 200 m. What
was the total braking time ?
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AP Physics
a) Our starting points are the equations of motion:
(1)
(2)
The following information is provided:
* v(t = 0) = v0 = 75 km/h = 20.8 m/s
* v(t1) = 45 km/h = 12.5 m/s
* x(t = 0) = x0 = 0 m (Note: origin defined as position of Porsche at t = 0 s)
* x(t1) = 88 m
* a = constant
From eq.(1) we obtain:
(3)
Substitute (3) in (2):
(4)
From eq.(4) we can obtain the acceleration a:
(5)
b) Substitute eq.(5) into eq.(3):
(6)
c) The car is at rest at time t2:
(7)
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AP Physics
Substituting the acceleration calculated using eq.(5) into eq.(3):
(8)
d) Substitute t2 (from eq.(8)) and a (from eq.(5)) into eq.(2):
(9)
e) The following information is provided:
* v(t3) = 0 m/s (Note: Porsche at rest at t = t3)
* x(t = 0) = x0 = 0 m (Note: origin defined as position of Porsche at t = 0)
* x(t3) = 200 m
* a = constant = - 1.6 m/s2
Eq.(1) tells us:
(10)
Substitute eq.(10) into eq.(2):
(11)
The time t3 can now easily be calculated:
(12)
2.5. Gravitational Acceleration
A special case of constant acceleration is free fall (falling in vacuum). In problems of free fall, the direction of
free fall is defined along the y-axis, and the positive position along the y-axis corresponds to upward motion.
The acceleration due to gravity (g) equals 9.8 m/s2 (along the negative y-axis). The equations of motion for free
fall are very similar to those discussed previously for constant acceleration:
pg. 10
AP Physics
where y0 and v0 are the position and the velocity of the object at time t = 0.
Example
A pitcher tosses a baseball straight up, with an initial speed of 25 m/s. (a) How long does it take to reach its
highest point ? (b) How high does the ball rise above its release point ? (c) How long will it take for the ball to
reach a point 25 m above its release point.
Figure 2.4. Vertical position of baseball as function of time.
a) Our starting points are the equations of motion:
The initial conditions are:
* v(t = 0) = v0 = 25 m/s (upwards movement)
* y(t = 0) = y0 = 0 m (Note: origin defined as position of ball at t = 0)
* g = 9.8 m/s2
The highest point is obtained at time t = t1. At that point, the velocity is zero:
The ball reaches its highest point after 2.6 s (see Figure 2.4).
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AP Physics
b) The position of the ball at t1 = 2.6 s can be easily calculated:
c) The quation for y(t) can be easily rewritten as:
where y is the height of the ball at time t. This Equation can be easily solved for t:
Using the initial conditions specified in (a) this equation can be used to calculate the time at which the ball
reaches a height of 25 m (y = 25 m):
t = 1.4 s
t = 3.7 s
Figure 2.5. Velocity of the baseball as function of time.
The velocities of the ball at these times are (see also Figure 2.5):
v(t = 1.4 s) = + 11.3 m/s
v(t = 3.7 s) = - 11.3 m/s
At t = 1.4 s, the ball is at y = 25 m with positive velocity (upwards motion). At t = 2.6 s, the ball reaches its
highest point (v = 0). After t = 2.6 s, the ball starts falling down (negative velocity). At t= 3.7 s the ball is
located again at y = 25 m, but now moves downwards.
pg. 12
AP Physics
Given below is a strobe picture of a ball rolling across a table. Strobe pictures reveal the position of the object at regular
intervals of time, in this case, once each 0.1 seconds.
Notice that the ball covers an equal distance between flashes. Let's assume this distance equals 20 cm and display the
ball's behavior on a graph plotting its x-position versus time.
The slope of this line would equal 20 cm divided by 0.1 sec or 200 cm/sec. This represents the ball's average velocity as it
moves across the table. Since the ball is moving in a positive direction its velocity is positive. That is, the ball's velocity is a
vector quantity possessing both magnitude (200 cm/sec) and direction (positive).
The following physlet by John M. Clement will allow you to test your understanding of this relationship between an object's
linear motion and the graphical representation of its behavior.
Position-Time Physlet
Animation created by John M. Clement © 2000 all rights reserved.
Given below are five combinations of position-time graphs for one-dimensional motion. On each graph, the slope
represents the object's velocity.
s vs t - the object is standing still at a positive location. Since the slope equals zero it
has no movement.
pg. 13
AP Physics
s vs t - the object is traveling at a constant positive velocity. The locations of its
position are increasingly positive.
s vs t - the object is traveling at a constant positive velocity but is traveling through a
negative region. For example, a car is traveling north on South Clyde Morris Boulevard
towards International Speedway.
s vs t - this slope represents a constant negative velocity since the object is traveling
in a negative direction at a constant rate. Notice that the locations of its position are
becoming less and less positive.
s vs t - the object is traveling at a constant negative velocity through a negative
region. For example, a car is traveling south on South Clyde Morris Boulevard towards
Dunlawton. The locations of its position are increasingly negative.
pg. 14
AP Physics
Assignment #3
During which intervals was he traveling in a positive direction?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
7 to 9 sec
9 to 11 sec
7 to 9 sec
9 to 11 sec
7 to 9 sec
9 to 11 sec
7 to 9 sec
9 to 11 sec
During which intervals was he traveling in a negative direction?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
During which interval was he resting in a negative location?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
During which interval was he resting in a positive location?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
During which two intervals did he travel at the same speed?
0 to 2 sec
2 to 5 sec
5 to 6 sec
6 to 7 sec
7 to 9 sec
9 to 11 sec
Refer to the following information for the next eight questions.
pg. 15
AP Physics
What was his average speed in the first 5 seconds?
What was his average speed in the last 5 seconds?
What was his average velocity during the first 8 seconds?
What was his average velocity from 6 to 10 seconds?
What total distance did he travel?
What was his average speed for the entire 11 seconds?
What was his net displacement for the entire 11 seconds?
What was his average velocity for the entire 11 seconds?
pg. 16
AP Physics
Scalars and Vectors
pg. 17
AP Physics
Assignment # 4
Directions: On this worksheet you will practice adding vectors. Remember that vectors are added graphically by using
the head-to-tail method and that the resultant is the vector that connects the beginning of the first vector to the end of the
final vector. You will be asked questions regarding each resultant's magnitude and direction. The example vectors
displayed in the table below are not drawn to scale; however, they do indicate correct relative directions.
x
z
a
b
Question 1 Given the vectors: x = (17 meters, 0º) and z = (6 meters, 0º).
omit
What is the magnitude, or length, of R1 = x + 2z?
Question 2 What is the magnitude, or length, of R2 = 4x - z?
omit
NOTE: subtracting a vector means that you should add a vector that has the same
magnitude, but points in 180º the opposite direction.
omit Question 3 What is the direction of R3 if R3 = - R2
Question 4 Given the vectors: x = (17 meters, 0º) and a = (6 meters, 40º)
omit
What is the magnitude, or length, of R4 = x + 3a?
omit Question 5 What is the direction of R4 in degrees?
Question 6 Given the vectors: a = (10 meters, 40º) and b = (23 meters, 90º)
omit
What is the magnitude, or length, of R5 = 4a - 2b
omit Question 7 What is the direction of R5 in degrees?
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AP Physics
Assignment # 5
Directions: On this worksheet you will practice with the basic definitions of introductory motion.
Question 1 A bike messenger traveled 3 blocks North, 4 blocks East, 6 blocks South, and
omit finally 8 blocks West in order to deliver a package in the traffic, congested city. If his trip
took 46 minutes, what was the magnitude of his average velocity in blocks/minute?
5 x 100
1.09 x 10-1
4.57 x 10-1
1.52 x 10-1
2.1 x 101
Question 2 If the messenger in Question #1 could have traveled directly to his
omit destination, what would have been the direction of his net displacement?
216.9 deg
143.1 deg
149.0 deg
126.9 deg
211.0 deg
Question 3 The magnitude of an object's average velocity can ONLY equal the magnitude
omit of its average speed when the object is
traveling in a
circle
traveling in
successive
directions that change by
90º
traveling in
a
straight line
standing
still
omit Question 4 A scalar is a quantity that can be completely described by stating its
size and direction
direction
size
Question 5 A family taking a vacation traveled 4 hours at 65 mph and then 3 hours at only
omit 49 mph. What was their average speed during this trip?
48.7 mph
57.0 mph
55.9 mph
58.1 mph
omit Question 6 Which quantity is NOT a scalar?
mass
time
distance
acceleration
Question 7 Which description of an object's motion is more specific: moving at a constant
omit speed or moving at a constant velocity?
they are
equivalent
constant speed since it
demands that the object has to
maintain a constant rate regardless
of its direction of motion
constant velocity since it
demands that the object not only
move at a constant rate, but also
maintain a constant direction
pg. 19
AP Physics
Question 8 A student warming up for practice travels one full circuit, 400 meters, around
omit the track. Initially he jogs 92 meters at 1.5 m/sec, then runs 276 meters at 2.2 m/sec, and
finally cools down by finishing the final 32 meters at 1.0 m/sec. What was his average
speed?
1.83 m/sec
2.35 m/sec
1.57 m/sec
1.94 m/sec
omit Question 9 What was the student's average velocity in Question #8?
the same as his average speed
0 m/sec
cannot be determined
Question 10 During a 30 minute period of time, one car moves at a constant velocity of 45
omit mph, N, while a second car moves at a constant velocity of 45 mph, W. During this time
interval, the cars would have the same
A. instantaneous
speed
A and C
B. instantaneous
velocity
B and C
C.
displacement
A and D
C and D
D.
acceleration
B and D
Question 11 A moving van completes its journey of 690 kilometers in 8 hours.
omit Approximately how far should it have traveled 6 hours after beginning its trip?
115 km
173 km
518 km
388 km
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AP Physics
Assignment #6
First, read each problem carefully. Then check each box to show which givens were supplied in the problem's statement.
On your papers, write down all of your givens as well as which variable represents the requested solution. You should
next write down the formula that you think will permit you to solve the problem. Finally, substitute in your givens, show
your mathematical solution process, and box in your numerical answer with its appropriate units. Don't forget to check
your final numerical answer online.
Refer to the following information for the next five questions.
1. An Indy-500 race car's velocity increases from 4.00 m/sec to 36.0 m/sec over an interval lasting 4.00 seconds.
Which kinematics variables are stated in this problem?
vo
vf
a
s
t
initial velocity final velocity acceleration displacement time interval
(a) What is the car's average acceleration?
Which kinematics equation did you use to solve this problem?
(b) How far does the car travel during this amount of time?
At this point in your solution, which kinematics equations are available for you to use to solve for the displacement?
Refer to the following information for the next five questions.
2. A golf ball rolls up a hill towards a putt-putt hole. It leaves the club traveling +2.0 m/sec and experiences an
acceleration of - 0.50 m/sec2.
(a) What will be its velocity after it has been rolling for three seconds?
Which kinematics variables were stated in this problem?
vo
vf
a
s
t
initial velocity final velocity acceleration displacement time interval
Which kinematics equation did you use to solve this problem?
(b) What will be its velocity after it has been rolling for a total of five seconds?
(c) Explain what happened to the ball between three and five seconds.
Refer to the following information for the next three questions.
3. While gliding down a steep hill, a bike rider experiences constant acceleration. After 4.50 seconds, he reaches a final
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AP Physics
velocity of 7.50 m/sec. The bike's displacement was 19.0 meters.
Which kinematics variables are stated in this problem?
vo
vf
a
s
t
initial velocity final velocity acceleration displacement time interval
How fast was the bike traveling when it first started down the hill?
Which kinematics equation did you use to solve this problem?
Refer to the following information for the next five questions.
4. An airplane starts from rest and accelerates at a constant 3.00 m/sec 2 for 30.0 seconds before leaving the ground at
the end of the runway.
Which kinematics variables are stated in this problem?
vo
vf
a
s
t
initial velocity final velocity acceleration displacement time interval
(a) How long was the runway?
Which kinematics equation did you use to solve this problem?
(b) How fast was the plane moving when it "lifted off" the ground at the end of the runway?
At this point in your solution, which kinematics equations are available for you to use to solve for the final velocity at
liftoff?
Refer to the following information for the next three questions.
5. An airplane while in flight, accelerates from a velocity of 21.0 m/sec at a constant rate of 3.00 m/sec 2 over a total of 535
meters.
Which kinematics variables are stated in this problem?
vo
vf
a
s
t
initial velocity final velocity acceleration displacement time interval
What was its final cruising velocity?
Which kinematics equation did you use to solve this problem?
Refer to the following information for the next two questions.
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AP Physics
6. Statistically, a person wearing a shoulder harness can survive a car crash if the acceleration is smaller than - 300.
m/sec2. Assuming a constant acceleration, how far could the front end of a car collapse if the car impacts while going 28.0
m/sec and comes to a complete stop?
s=
Which kinematics equation did you use to solve this problem?
Refer to the following information for the next two questions.
7. If a bullet leaves the muzzle of a rifle with a speed of 600. m/sec, and the barrel of the rifle is 0.900 meters long, what is
the acceleration of the bullet while in the barrel?
a=
Which kinematics equation did you use to solve this problem?
pg. 23
AP Physics
Gizmo
Complete all gizmos.
Go to www.explorelearning.com
Enroll in class. Class code: QPYNNAFQQT
Create an account.
Use your first and last name as your username (FYI: I can see your username and password in case you forget.)
pg. 24