As you come in. Pick up graded homework from front Turn in homework in the box

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1 As you come in Pick up graded homework from front Turn in homework in the box

2 LECTURE 3 CONTINUING CHAPTER 2 Professor Cassandra Paul

3 How I graded homework I was thorough and lenient! A s (4.0) were given if it was complete, and thought was given to every question C s (2.0) were given if a number of problems were not completed, or no work was included (or late) F s (zeros) were only given if you turned nothing in Pay attention to comments, and if I suggest you come to office hours, please do! Common issues: Polar coordinates Free fall Velocity/acceleration confusion

4 Did not receive homework from Galaviz Hamilton Moua T. Nguyen Ochoa Ngo If you are not officially added yet, your name might not be listed here even though I have not received homework from you.

5 Before we start Get in small groups (lets try 3) Discuss any issues you had with the homework Help your group-mates with their difficulties (5 minutes)

6 Any further Issues: See me in office hours Make an appointment with me Set up a time to meet with some classmates Ask your workshop facilitator for help Physics Club? Peer connections (drop in tutoring):

7 Groups of 5 Name tags up White boards, markers, erasers Clickers

8 Last time: Multiple choice An object with a positive velocity (+3m/s for example) indicates the object must: A. Be speeding up B. Be traveling in a positive direction C. Have a positive acceleration D. Have a positive displacement E. Both A & B

9 Multiple choice An object with a positive velocity (+3m/s for example) indicates the object must: A. Be speeding up B. Be traveling in a positive direction C. Have a positive acceleration D. Have a positive displacement E. Both A & B v=δx/t t is always positive therefore if v is positive Δx is also positive

10 Multiple choice An object with a positive velocity (+3m/s for example) indicates the object must: A. Be speeding up B. Be traveling in a positive direction C. Have a positive acceleration D. Have a positive final distance E. Both A & B

11 Unit Conversion Convert 20 inches to centimeters: *Remember multiplying by 1 gives us the same quantity back! 5 x 1 = inches x 2.54 centimeters 1 inch Learn this! = 20.0 x 2.54 = 50.8 centimeters Updated since class: correct values and sig figs

12 You try: Convert 100 miles/hour into meters/second 1 mile ~ 1610 meters 100 miles x 1 hour x 1 min x 1610 meters hour 60 min 60 sec 1 mile = meters second

13 Position, Velocity & Acceleration vs. Time graphs Δx = x f x i v = Δx / Δt a = Δv /Δt Case 1: A student walking across campus to class at a constant speed. x Distance changing at a constant rate. v Velocity is constant and positive. a Acceleration is zero because velocity is not changing. t t f t t f t t f

14 Case 2: Dr. Paul bicycling down San Fernando. x v a t t 4 t t f t t f

15 Check-In Clicker question A. I am very confident in my understanding of these graphs and ability to produce them B. I think I might need to study a bit more, but I feel ok with them C. I will need to seek help to learn these D. I am completely lost

16 Velocity v = Δx / Δt Average Velocity v = lim Δx / Δt Δt 0 Instantaneous velocity

17 Review on Limits Δx/Δt = rise/run = slope x (t 2, x 2 ) (t 1, x 1 ) t

18 Review on Limits Δx/Δt = rise/run = slope x (t 2, x 2 ) (t 1, x 1 ) t

19 Review on Limits Δx/Δt = rise/run = slope x (t 2, x 2 ) (t 1, x 1 ) t

20 Review on Limits v = lim Δs / Δt Δt 0 x (or v=dx/dt in calculus) t the line tangent to the position vs. time graph is defined to be the instantaneous velocity at that time

21 v = lim Δx / Δt Δt 0 (or v=dx/dt) x x t t f t t f the line tangent to the position vs. time graph is defined to be the instantaneous velocity at that time

22 x x t t f t t f This is why why we often calculate average velocity and not instantaneous velocity.

23 When you are asked to find instantaneous velocity what do you do? x x t t 1 t t 2

24 Graphical Instantaneous Velocity Average velocities are the blue lines The green line (tangent) is the instantaneous velocity Section 2.2

25 Instantaneous Velocity The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero The instantaneous velocity indicates what is happening at every point of time The magnitude of the instantaneous velocity is what you read on a car s speedometer Section 2.2

26 Acceleration Average Acceleration a = lim Δv/ Δt = Δt 0 Instantaneous Acceleration

27 You try: In groups of 5 use your white boards to graphically represent Be as accurate as possible!

28 Free Fall A freely falling object is any object moving freely under the influence of gravity alone Free fall does not depend on the object s original motion All objects falling near the earth s surface fall with a constant acceleration The acceleration is called the acceleration due to gravity, and indicated by g Section 2.6

29 Free Fall g = acceleration due to gravity g x mass = weight = force of the earth pulling on you Convention: The direction of the pull of the earth is downwards, therefore a = -g = (in the y direction)

30 Common Confusions Pg 43 : The value of g decreases with increasing altitude. at Earth s surface g is equal to 9.81m/s G varies for VERY large distances, it s negligible at Earth s surface

31 Gravity San Jose State, Elevation: 85ft g = 9.81 University of Wyoming, Elevation: 7200 ft g = 9.79

32 Clicker Question Which of the following is true? For a freely falling object: A. Acceleration is always downwards B. Acceleration is downwards only when the object is traveling downwards (past max height) C. Acceleration is zero at max height D. Acceleration is constant E. Both A and D

33 Homework: Chapter 2 problems : 6, 20, 24, 35, 45, 47, 51 Read Chapter 3: take notes, work examples Chapter 3: Conceptual Questions : 1, 3, 4, 7, 10, 11

Chapter 1 Problem 28: Agenda. Quantities in Motion. Displacement Isn t Distance. Velocity. Speed 1/23/14

Chapter 1 Problem 28: Agenda. Quantities in Motion. Displacement Isn t Distance. Velocity. Speed 1/23/14 Agenda We need a note-taker! If you re interested, see me after class. Today: HW Quiz #1, 1D Motion Lecture for this week: Chapter 2 (finish reading Chapter 2 by Thursday) Homework #2: continue to check