AP Physics I Summer Assignment
IMPORTANT MESSAGE: This assignment will not be a part of your grade,
however, you will be given an exam over summer assignment on the first day of AP
Physics I class and it will be your first major grade.
1. Scientific Notation:
The following are ordinary physics problems. Write the answer in scientific notation and simplify the units (π=3).
4.5  102 kg

2.0  103 kg s2
a.
Ts  2
b.
2
3.2 109 C 9.6 109 C

9 N m 
F   9.0 10


2
C2 
 0.32m 

𝐹=_______________
c.
1
1
1


2
Rp 4.5  10  9.4  102 
𝑅𝑝 =_______________
d.
Kmax  6.63 1034 J  s 7.09 1014 s  2.17 1019 J 
𝐾𝑚𝑎𝑥 =_______________
e.
 
𝛾=_______________
f.
K
𝑇𝑠 =_______________


2.25  108 m s
1
3.00  108 m s



1
6.6×102 kg 2.11×104 m s
2
AP Physics I, Summer Assignment

RP 

1



2

𝐾=_______________
1
g.
1.33 sin 25.0  1.50 sin 
𝜃=_______________
2. Solving Equations:
Often problems on the AP exam are done with variables only. Solve for the variable indicated. Don’t let the
different letters confuse you. Manipulate them algebraically as though they were numbers.
1 2
kx
2
a.
K
, x  _______________
b.
Tp  2

g
, g  ______________
c.
Fg  G
m1m2
r2
, r  _______________
d.
mgh 
1 2
mv
2
, v  _______________
e.
x  xo  vot 
1 2
at
2
o I
2 r
,r 
_______________
,d 
_______________
, t  _______________
f.
B
g.
xm 
h.
pV  nRT
, T  _______________
i.
sin  c 
n1
n2
, c  _______________
mL
d
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j.
3.
qV 
1 2
mv
2
,v 
_______________
Conversion
Science uses the KMS system (SI: System Internationale). KMS stands for kilogram, meter, second. These are the
units of choice of physics. The equations in physics depend on unit agreement. So you must convert to KMS in
most problems to arrive at the correct answer.
kilometers (km) to meters (m) and meters to kilometers
centimeters (cm) to meters (m) and meters to centimeters
gram (g) to kilogram (kg)
Celsius (oC) to Kelvin (K)
millimeters (mm) to meters (m) and meters to millimeters
nanometers (nm) to meters (m) and metes to nanometers
micrometers (m) to meters (m)
Other conversions will be taught as they become necessary.
atmospheres (atm) to Pascals (Pa)
liters (L) to cubic meters (m3)
What if you don’t know the conversion factors? Colleges want students who can find their own information (so do
employers). Hint: Try a good dictionary and look under “measure” or “measurement”. Or the Internet? Enjoy.
6.23x10-7 m
a.
4008 g
= _______________ kg
l.
b.
1.2 km
= _______________ m
m. 1.5x1011 m
c.
823 nm
= _______________ m
d.
298 K
= _______________ oC
e.
0.77 m
= _______________ cm
f.
8.8x10-8 m
= _______________ mm
g.
1.2 atm
= _______________ Pa
h.
25.0 m
= _______________ m
i.
2.65 mm
= _______________ m
j.
8.23 m
= _______________ km
k.
40.0 cm
= _______________ m
= _______________ nm
= _______________ km
4. Geometry
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Solve the following geometric problems.
a. Line B touches the circle at a single point. Line A extends through the center of the circle.
i.
What is line B in reference to the circle?
B
_______________
ii.
How large is the angle between lines A and B?
A
_______________
b. What is angle C?
C
30o
_______________
45o
c.
What is angle  ?
30o

_______________
d. How large is ?
_______________

30o
e.
The radius of a circle is 5.5 cm,
i. What is the circumference in meters?
ii.
f.
_______________
What is its area in square meters?
_______________
What is the area under the curve at the right?
4
_______________
12
20
5. Trigonometry
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Using the generic triangle to the right, Right Triangle Trigonometry and
Pythagorean Theorem solve the following. Your calculator must be in degree
mode.
g.
 = 55o and c = 32 m, solve for a and b.
_______________
h.
 = 45o and a = 15 m/s, solve for b and c.
_______________
i.
b = 17.8 m and  = 65o, solve for a and c.
_______________
j.
a = 250 m and b = 180 m, solve for  and c.
_______________
k.
a =25 cm and c = 32 cm, solve for b and .
_______________
l.
b =104 cm and c = 65 cm, solve for a and .
_______________
Vectors
Most of the quantities in physics are vectors. This makes proficiency in vectors extremely important.
Magnitude: Size or extend. The numerical value.
Direction: Alignment or orientation of any position with respect to any other position.
Scalars: A physical quantity described by a single number and units. A quantity described by magnitude only.
Examples: time, mass, and temperature
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Vector: A physical quantity with both a magnitude and a direction. A directional quantity.
Examples: velocity, acceleration, force
Notation: A
A
or
Length of the arrow is proportional to the vectors magnitude.
Direction the arrow points is the direction of the vector.
Negative Vectors
Negative vectors have the same magnitude as their positive counterpart. They are just pointing in the
opposite direction.
A
A
Vector Addition and subtraction
Think of it as vector addition only. The result of adding vectors is called the resultant. R
A B  R
A
+
B
R
=
So if A has a magnitude of 3 and B has a magnitude of 2, then R has a magnitude of 3+2=5.
When you need to subtract one vector from another think of the one being subtracted as being a negative
vector. Then add them.
A negative vector has the same length as its positive counterpart, but its direction is reversed.
So if A has a magnitude of 3 and B has a magnitude of 2, then R has a magnitude of 3+(-2)=1.
This is very important.
In physics a negative number does not always mean a smaller number.
Mathematically –2 is smaller than +2, but in physics these numbers have the same magnitude (size), they just point
in different directions (180o apart).
There are two methods of adding vectors
Parallelogram
A+B
A
A
A
R
B
B
B
A–B
A
R
A
B
-B
Tip to Tail
A+B
-B
B
A
B
A
B
A–B
A
A
-B
R
-B
A
B
R
A
A
6. Drawing Resultant Vectors
Draw the resultant vector using the parallelogram method of vector addition.
Example
a.
AP Physics I, Summer Assignment
b.
6
c.
d.
e.
Draw the resultant vector using the tip to tail method of vector addition. Label the resultant as vector R
Example 1: A + B
B
B
A
A
R
-B
Example 2: A – B
A
B
A
f.
R
X+Y
g.
T–S
h.
P+V
X
Y
T
S
P
V
C–D
i.
C
D
Component Vectors
A resultant vector is a vector resulting from the sum of two or more other vectors. Mathematically the
resultant has the same magnitude and direction as the total of the vectors that compose the resultant. Could a
vector be described by two or more other vectors? Would they have the same total result?
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This is the reverse of finding the resultant. You are given the resultant and must find the component vectors
on the coordinate axis that describe the resultant.
R
+Ry
R
R
+Rx
or
+Ry
+Rx
Any vector can be described by an x axis vector and a y axis vector which summed together mean the exact
same thing. The advantage is you can then use plus and minus signs for direction instead of the angle.
7. Resolving a vector into its components
For the following vectors draw the component vectors along the x and y axis.
a.
c.
b.
d.
Obviously the quadrant that a vector is in determines the sign of the x and y component vectors.
8. GRAPHS
AP Physics I, Summer Assignment
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A. Reading: Motion Maps
A motion map represents the position, velocity, and acceleration of an object at various clock readings.
Suppose that you took a stroboscopic picture of a car moving to the right at constant velocity where each image revealed the
position of the car at one-second intervals.
This is the motion map that represents the car. We model the position of the object with a small point. At each position, the
object's velocity is represented by a vector.
If the car were traveling at greater velocity, the strobe photo might look like this:
The corresponding motion map has the points spaced farther apart, and the velocity vectors are longer, implying that the car is
moving faster.
If the car were moving to the left at constant velocity, the photo and motion map might look like this:
More complicated motion can be represented as well.
Here, an object moves to the right at constant velocity, stops and remains in place for two seconds, then moves to the left at a
slower constant velocity.
Consider the interpretation of the motion map below. At time t = 0, cyclist A starts moving to the right at constant velocity, at
some position to the right of the origin.
Cyclist B starts at the origin and travels to the right at a constant, though greater velocity.
At t = 3 s, B overtakes A (i.e., both have the same position, but B is moving faster).
B. Graph Analysis
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A graph is one of the most effective representations of the relationship between two variables. The independent
variable is usually placed on the x-axis. The dependent variable is usually placed on the y-axis. It is important for
you to be able interpret a graphical relationship and express it in a written statement and by means of an algebraic
expression.
Graph Shape
Written Relationship
Modification
Required to liberalize
graph
Algebraic
representation
When you state the relationships, tell how y depends on x (e.g., as x increases, y …).
In each table below, the motion is described by a position (x) -vs-time graph, a velocity (v) -vs-time graph,
a verbal description or a motion map. The other three representations have been left blank.
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Complete the missing representations. Be sure to include each of the following in your verbal description:
starting position, direction moved, type of motion, relative speed.
1-
Written Description:
b
Motion Map:
2-
Written Description:
b
Motion Map:
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3-
Written Description:
b
Motion Map:
4-
Written Description: The object starts close to the motion detector,
and moves at a constant, moderate speed in the forward direction for
several seconds. Then it stops for a few seconds before returning to
its starting point, once again at a moderate speed.
b
Motion Map:
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