AP Physics C implements the study of calculus to analyze physical situations and describe natural phenomena. All students enrolled in AP Physics C are required to either have taken calculus (honors, AB, or BC) or be concurrently enrolled in calculus. At the end of last year's mathematics course, students should have started their calculus studies with the introduction of derivatives. This packet will work through some of the basic calculus needed for this course. I strongly suggest that you work though as much of this packet as you can before we start class. We will go over these concepts the first couple days of class and follow it with a quiz. If you have not yet taken calculus at the very least, familiarize yourself with the power rule and chain rule and work through the first two pages. I recommend that you complete this packet towards the end of your summer, rather than the beginning. 1. Give an expression for the average velocity of a particle whose position is given by Sat+bt + ct + d. The average is from t=0 to time t; a, b, c, and d are constants. (Note that this does not require a derivative.) 2. An object moves so that its position is given by S= So sin(7rt). Where S and So are in meters, t is in seconds, and the angle is in radians. So is a constant. If So= 5.7, what is its instantaneous velocity at t = 8.0 s? 3. Find the instantaneous velocity of a particle in terms of a and b (both are constants) whose position is given by S at+bt when t= 18 s.