Tuscarora High School AP Physics C: Mechanics Summer Assignment

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Bonnie Watts
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1 Tuscarora High School AP Physics C: Mechanics Summer Assignment Welcome to AP Physics. Here is the summer assignment along with a little bit about the beginning of the school year. Summer Assignment: The summer assignment has five parts. 1. Algebra This is a review of material everyone should have seen before from algebra 2 and precalculus. 2. Trigonometry This is a review of material everyone should have seen before in either algebra 2/trig or precalculus. 3. Data/Data Analysis This is a review of material presented in academic physics and also in various math classes. 4. Beginning Calculus For students who have not taken calculus prior to senior year, these will be difficult. Spend some time trying to learn and understand the basics of calculus on your own. If you are able to do this, then you will be prepared well for the first day of class. 5. Calculus This part of the assignment is geared toward the students who have already completed calculus. I encourage students who have not taken calculus to attempt these problems, but they will be difficult. The summer assignment is worth 100 points and is due in the third week of class. The first three parts will be graded for accuracy, and the fourth part will be graded for completion. The final part will be a bonus assignment. You do not have to be an expert in calculus by the end of the summer. However, the more calculus you have been exposed to and understand, the easier the first couple months of class will be. Please complete this assignment on separate paper. Note that if insufficient work is shown because it was all done on your calculator, your calculator will be credited with half the points for the summer assignment. It is critical to show work on the AP exam in May. Beginning of school: The first 3 to 4 weeks of school will be a crash course in vector math and calculus. We need to understand the basics of calculus before we can do beginning physics questions. For students who have taken calculus, this will be a great time to fortify previous concepts. Students who are taking calculus for the first time, this will be a difficult few weeks. We will be setting the foundation for the rest of the school year. Enjoy your summer. When the school year starts, it will be full speed ahead until the AP test in May. If you have questions, me at Michael.Sheaffer@lcps.org. I should be available to answer questions for the summer except for the first two weeks of July when I am out of the country. --Mr. Sheaffer

2 Part 1 Algebra Solve for the variable in parentheses 1. (v o ) 2. 2 (x) 3. (v o ) 4. (m 2 ) 5. (r) (L) (d o ) (v) 2 (x) Part 2 Trigonometry/Geometry 10. Show that 1 for angles between -π/2 and π/2 11. Show that cos sin sincos 1 (use the formula for sums of angles) 12. Solve for θ between 0 and 2π: 2sin sin The area of a circle is 5 square meters. What is its area in square centimeters?

3 Part 3 Data/Data Analysis 14. Plot a graph for the following data recorded for an object falling from rest. a. What kind of curve did you obtain? b. What is the relationship between the variables? c. What do you expect the velocity to be after 4.5 seconds? d. How much time is required for the object to reach ft/s?

4 15. Plot a graph showing the relationship between frequency and wavelength of electromagnetic waves a. What kind of curve did you obtain? b. What is the relationship between the variables? c. What do you expect the wavelength of an electromagnetic wave of frequency 350 khz? d. What is the frequency of an electromagnetic wave with wavelength 375 m?

5 16. In an experiment with circuits, the following data was recorded. Plot a graph with the data: a. What kind of curve did you obtain? b. What is the relationship between the variables? c. What is the power when the current is 3.2 A? d. What is the current when the power is 64.8 W?

6 Part 4 Beginning Calculus If you need help with calculus, the following videos on Khan Academy are what you will need to know for this course. DO NOT BE INTIMIDATED BY THE CALCULUS. The calculus we need is a lot simpler than presented. Derivative as slope of a tangent line Derivative as instantaneous rate of change Basic differentiation rules Power rule Polynomial functions differentiation Rational functions differentiation Radical functions differentiation Sine & cosine derivatives e x and ln(x) derivatives Product rule Chain rule Quotient rule Trigonometric functions differentiation Exponential functions differentiation Logarithmic functions differentiation Higher-order derivatives Critical points Increasing & decreasing intervals Relative minima & maxima Absolute minima & maxima Concavity Points of inflection Sketching graphs using calculus Optimization Antiderivatives Indefinite integrals intro Indefinite integrals of common functions Definite integral as area Definite integral properties Integration by parts u-substitution Reverse chain rule Partial fraction expansion Area between curves Arc length Average value of a function Area & net change

7 Find the following limits, if they exist. 17. lim 18. lim 19. lim An object moves so that its position is given by, where a, b, c, and d are constants. 20. Write an expression for the average velocity from the particle from t = 0 to t = T in terms of T and the given constants. 21. Write an expression for the instantaneous velocity of the particle at time t = T in terms of T and the given constants. Find the derivative of each of the following functions with respect to its appropriate variable. Find: cos 25. ln For the function What is the first derivative of the function? 28. Determine where the local minimum or maximum occurs. 29. Determine the value of the local minimum or maximum. 30. What is the second derivative of the function? 31. Is the value found in #29 a minimum or a maximum?

8 Part 5 Calculus Evaluate the following indefinite integrals. Do not forget to include the constants of integration. 32. cos cos sin Evaluate the following definite integrals: / 37. sin cos Solve the following word problems: 39. Bob leaves for a trip at time t = 0 and drives with a speed described by the function Calculate the distance Bob travels in 2 hours, where v is in meters/second and t is in seconds. 40. Shauna starts painting at noon. She can paint (140-kt) square feet per hour, where t is the number of hours since she started painting and k is a constant accounting for the fact that Shauna slows down as she gets tired. If Shauna paints 100 square feet between 2 PM and 3 PM, what is k?

Curriculum Map: Mathematics

Curriculum Map: Mathematics Course: Calculus Grade(s): 11/12 Unit 1: Prerequisites for Calculus This initial chapter, A Prerequisites for Calculus, is just that-a review chapter. This chapter will provide