AP Physics C
Summer Assignment 2015
Welcome to AP Physics C! This packet is designed to keep your mind sharp over the summer and remind
you of some of the foundational skills we will be using throughout the course. It can also serve as a selfassessment in order to help you identify what skills you may need help with. We won’t have time to
cover these topics during the course because we want to jump right into the Physics.
It is expected that you will complete this packet. Do every problem. You will be graded on the effort
you put into the packet not necessarily the results, so do your best work. This will be your first grade of
MP 1 and count as a homework grade. Due date is the 1st week of class in August. My email is
jlmott@aacps.org : Mr. Mott
Part 1: Extra Resources
You will need additional help beyond the classroom in this course. Please find and list some resources,
books, websites, online videos, etc. that you find will help your learning style in this class.
Part 2: Equation Tables
The AP Physics C exam in 2015 allowed the use of the tables for the entire exam for the first time. You
will use these tables every class. Identify the equations that you are familiar with. Group the equations
that seem related.
Part 3: Physics in Everyday Life
Write about how physics is applied in your life. Did you surf? Drive a car? Explain in a paragraph
Part 4: Math review – Vector Algebra, Calculus, Separation of Variables & Differential Equations
Algebra: Manipulation of formulas and equations is essential for success in solving Physics problems.
1. Solve for x
2. Solve for x
4x  3  17
0.8  0.52x  0.98x  5.3
3. Solve for y
4. Solve for x and y (Systems of Linear Equations)
y 2  3 y  10
8 x  3 y  3
4 x  2 y  4
5. Solve for z
6. Solve for d (Most of Physics is solved symbolically)
3 z2
c
b
a
d
7. Define and explain dot product and cross product, and if they are commutative or associative.
Significant Figures and Scientific Notation: For accuracy purposes and ease of writing.
Indicate the number of significant figures and express in scientific notation (rounded to 2 decimal places)
1. 0.0845 kg
2. 8630000.000 mi
3. 2.9910 m
AP Physics C
Summer Assignment 2015
4. 5600 km
5. 809 g
Solve the following problems and give the answer in the correct number of significant digits & units.
6. 2.674 m / 2.0 m = ______________
7. 5.25 m x 1.3 m =________________
8. 9.0 cm + 7.66 cm + 5.44 cm = _________________
9. (3.0 x 104)(34.5 x 1012) = __________________
10. (2.64 x 10 6)/(5.67 x 10 -3) = ________________
Write the following out in decimal form
11. 1.23 x 10 -5
12. 7.543 x 106
Conversions: Important because there are several different systems of measure with variations of
measurements within each. When calculating, the measurements must be compatible (unit or
dimension analysis).
1. Convert 4.4 km/h to m/s.
2. Convert 8.76 x 107 MW to GW:
3. Convert 2.5 days to s:
4. Convert 22 mg to kg
5. 1 h to s
6. One light year is the distance light travels in one year. This distance is equal to
9.461 X 1015 m. The star Alpha Centuri, which is the nearest star to Earth that is visible to the
unaided eye, is about 4.35 light years away. Express this distance in
a. Gigameters
b. Picometers
Calculus: life isn’t always smooth. It can be varied, so calculus helps us analyze those situations as well.
1. If the function x=3t2– 6t +8 represents the position of a particle at any given time t. What
would the rate in change of position with time be? What does this represent? Show all work.
2. If the acceleration of a particle was represented by the function a(t) = 6t +2 and the area under
the graph of the function represents the velocity of the particle. What is the particles velocity
from t=0 to t=5 s.
Trigonometry: Important to break things into their component vectors.
Find the missing sides and angles in the following triangles:
12
22
12
9
70o
47°
AP Physics C
Summer Assignment 2015
Vectors: Physics happens in all three dimensions so we can analyze an event one dimension at a time.
Draw the following vectors and resolve them into their X and Y components:
1. 25 @ 30O
2. 40 @ 45o
3. 100 @ 120o
Graphing:
GRAPHING TECHNIQUES
Frequently an investigation will involve finding out how changing one quantity affects the value of
another. The quantity that is deliberately manipulated is called the independent variable. The quantity
that changes as a result of the independent variable is called the dependent variable.
The relationship between the independent and dependent variables may not be obvious from simply
looking at the written data. However, if one quantity is plotted against the other, the resulting graph
gives evidence of what sort of relationship, if any, exists between the variables. When plotting a graph,
take the following steps.
1. Identify the independent and dependent variables.
2. Choose your scale carefully. Make your graph as large as possible by spreading out the data on each
axis. Let each space stand for a convenient amount. For example, choosing three spaces equal to ten is
not convenient because each space does not divide evenly into ten. Choosing five spaces equal to ten
would be better. To avoid a cluttered appearance, you do not need to number every space.
3. All graphs do not go through the origin (0,0). Think about your experiment and decide if the data
would logically include a (0,0) point. For example, if a cart is at rest when you start the timer, then your
graph of speed versus time would go through the origin. If the cart is already in motion when you start
the timer, your graph will not go through the origin.
4. Plot the independent variable on the horizontal axis (x) and the dependent variable on the vertical
axis (y). Plot each data point.
5. Label each axis with the name of the variable and the unit.
6. If the data points appear to lie roughly in a straight line, draw the best straight line you can with a
ruler and a sharp pencil. Have the line go through as many points as possible with approximately the
same number of points above the line as below. Never "connect the dots." If the points do not form a
straight line, draw the best smooth curve possible.
7. Title your graph. The title should clearly state the purpose of the graph and include the independent
and dependent variables
Read the following carefully! The graph must be done on the graph paper section provided using good
graphing techniques!
Interpreting Graphs
In laboratory investigations, you generally control one variable and measure the effect it has on another
variable while you hold all other factors constant. For example, you might vary the force on a cart and
measure its acceleration while you keep the mass of the cart constant. After the data are collected, you
then make a graph of acceleration versus force using the techniques for good graphing. The graph gives
you a better understanding of the relationship between the two variables.
AP Physics C
Summer Assignment 2015
There are three relationships that occur frequently in physics. If the dependent variable varies directly
with the independent variable, the graph will be a straight line, as shown in graph A. If y varies inversely
with x, the graph will be a hyperbola as shown in graph B. The third relationship gives a parabola which
is represented by the square of x.
Graph Shape
Written Relationship
Modification required
to linearize graph
Algebraic
Representation
As x increases, y increases
proportionally.
Y is directly proportional
to x.
None
y = mx + b
As x increases, y
decreases.
Y is inversely proportional
to x.
Graph y vs 1/x or
y vs x-1
y = m(1/x) + b
Graph y vs x2
y = mx2 + b
Y is proportional to the
square of x.
Sometimes you need information about a value that you have not determined experimentally. Reading
from the graph between data points is called interpolation. Reading data points from the graph beyond
the limits of you experimentally determined is called extrapolation. Extrapolation must be used with
caution because you cannot be sure that the relationship between the variables remains the same
beyond the last data point.
1. The following data show the distance an object travels in certain time periods. Prepare a graph
showing these data.
Time (s)
0
1
2
3
4
Distance (m)
0
3
12
27
48
AP Physics C
Summer Assignment 2015
a) Describe the relationship between x and y as shown by your graph and write a general equation for
the curve.
b) Is the distance traveled greater between 0 s and 1 s or between 3 s and 4 s?
c) Is the slope of the curve greater between 1 s and 2 s or between 3 s and 4 s?
d) What is the slope of the curve between 1s and 2s? Remember to include units with your slope. Show
your work.
e) What is the slope of the curve between 3s and 4s? Remember to include units with your slope. Show
your work.
f) What physical quantity does the slope represent? (Hint: look at the units)
g) What real-life generalization can you make about the meaning of the slope of the line on this graph
(ex: The steeper the slope the ................................................. )?
AP Physics C
Summer Assignment 2015
AP Physics C
Summer Assignment 2015
AP Physics C
Summer Assignment 2015
AP Physics C
Summer Assignment 2015
AP Physics C
Summer Assignment 2015
AP Physics C
Summer Assignment 2015
Separation of Variables & Differential Equations:
Study how to separate variables to solve a differential equation. Show how to solve these 4 exercises.