1. Period 1 Pg. 29-31 Ques: 27, 33, 36, 56, 58a, 60-62, 66, 68b

2. Warm-Up Questions Just think, what is the difference between… – Speed & Velocity? – Distance & Displacement

4. 1-Dimensional Motion

5. Motion…(in a straight line) An object is in motion if… …it changes position …or… travels a distance How do we typically describe motion? – Speed Units…?? – Distance & Time -- Equation??

6. Speed vs. Velocity What’s the difference? – Speed = – Velocity = Difference btwn. Distance & displacement then? – Dist = total path length an object covered during its motion – Disp = directional distance between an object’s starting and ending points of motion -- Velocity Equation???

7. Scalar vs. Vector Quantities Scalar – Quantities that are described by magnitude alone Vector – Quantities that are described by BOTH a magnitude and direction

8. Examples: Scalar or Vector?? Distance = _______ Displacement = _______ Time = _______ Mass = _______ Velocity = _______ Speed = _______ Acceleration = _______

9. Vector Addition A vector is represented by an arrow – Drawn to scale and points in the direction of the motion – NET outcome = resultant vector ***Sum all the vectors in x direction & sum all vectors in y direction, then find magnitude of resultant vector Example: – A car drives 5 km east, stops, and drives another 3 km east. Draw the 2 initial vectors and the resultant vector.

10. Vector Addition A vector is represented by an arrow – Drawn to scale and points in the direction of the motion – NET outcome = resultant vector Example: – A car drives 2 km east, stops, drives 10 km west, stops, and then drives another 3 km east again. Draw the 3 initial vectors and the resultant vector.

11. ***Need to Know Equations*** Avg. Speed = Avg. Velocity = Final Position =

12. Question… A hiker walks 6 km west and then turns abruptly and immediately walks another 8 km north and stops to catch his breath. – What was the distance that he hiked so far? – What was the displacement of his hike so far?

13. Use Trig to find Direction A hiker walks 6 km west and then turns abruptly and immediately walks another 8 km north and stops to catch his breath. – What was the displacement of his hike so far?

14. Question A BPHS track star runs the 100 m turn (half circle portion at the end of the track) in 16 s. What distance did they run? Displacement? What was their speed? Velocity? **Circumference = 2 r **

15. Warm-Up Question A jogger jogs 300 m straight in one direction in 2.5 min and then jogs back to the starting point in 3.3 min. What was the jogger’s avg velocity: 1.On the way down? 1.On the way back to the starting point? 2.For the total jog?

16. Distance vs. Displacement Wkst

17. Instantaneous Velocity Defined as: – How fast something is moving in which direction at a particular instant of time When dealing with uniform motion, how are inst. velocity and avg. velocity related?

18. Graphical Representation

19. Nonuniform Motion How would you find the inst. velocity of an object’s motion that looked like: Position Time

20. Nonuniform Motion How would you find the inst. velocity of an object’s motion that looked like:

21. Nonuniform Motion How would you find the inst. velocity of an object’s motion that looked like:

22. Math Problems Book: – Pg. 60-61 -> 1, 7, 8, 10, 13-14, 16, 21, (22 = Bonus)

24. Acceleration Defined as: – Rate at which velocity changes Velocity changes when: – An object speeds up or slows down – An object changes its direction of motion So when does an object accelerate?

25. ***Need to Know Equations*** Avg. Acceleration = Final Velocity (w/ constant acceleration) =

26. Acceleration Math A car has an initial velocity of 80 m/s. It slows down to a stop in 8 seconds. What was the cars acceleration during this time?

27. Average Velocity Question… What was the average velocity of that car as it constantly accelerated during that time period?

28. ***Need to Know Equations*** Avg. Acceleration = Final Velocity (w/ constant acceleration) = Avg. Velocity (w/ constant acceleration) =

29. Math Problems Pg. 61-62  23-27, 30, 32-34

31. Kinematic Equations Some physics problems are hard to do because they require the application of multiple equations throughout one question. How can we make our lives easier…? – Let’s combine a couple of our equations algebraically in advance

32. Deriving Equations Final position w/o avg. velocity & acceleration: – X f eq: – Avg. V eq: – Combined (sub in for avg. v):

33. Deriving Equations Final position w/o avg. velocity & acceleration: x f = x i + ½(v f + v i )t

34. Deriving Equations Displacement when object accelerates w/o v f :

35. Deriving Equations Displacement when object accelerates w/o v f : – Use previous equation: – V f eq: – Combined (sub in for V f ):

36. Deriving Equations Displacement when object accelerates w/o v f : x f = x i + v i t + ½at 2

37. Deriving Equations Displacement when object accelerates from rest: x f = x i + v i t + ½at 2 x f = x i + ½at 2 x f = ½at 2

38. Deriving Equations Displacement, Velocity, & Acceleration w/o Time: – Use V f eq: – x f = x i + ½(v f + v i )t eq:

39. Deriving Equations Displacement, Velocity, & Acceleration w/o Time:

40. Deriving Equations Displacement, Velocity, & Acceleration w/o Time: v f 2 = v i 2 + 2a(x f – x i )

41. Example Math Problem A rocket is shot horizontally from a soldier’s rocket launcher with a constant acceleration of 20m/s 2. After 10 seconds, how fast is the rocket moving & how far has it traveled?

42. Example Math Problem A rocket is shot horizontally from a soldier’s rocket launcher with a constant acceleration of 20m/s 2. After 10 seconds, how fast is the rocket moving & how far has it traveled?

43. Math Problems Pg. 62  38 - 42

45. Additional Lab Questions What should the slope of the line for the graph that you drew be equal to? (Name & Value…think about rise over run) Knowing this, what equation can we then derive to solve for the acceleration of an object on an inclined plane? What was the percent error between the extrapolated value and the accepted value of g?

46. Free Fall Defined as: – When an object in motion is influenced only by the pull of gravity Value of Gravity = - 9.8 m/s 2

47. Gravity Does the acceleration of an object due to gravity ever change? – Acceleration due to g is constant! Constant acceleration = which equations??? Can it be different in different regions on Earth? – YES! Due to…. Distance from Earth’s center Air resistance

48. Free Fall Equations

50. Math Problems Pg. 63-64  59-62, 64-67, 70a

52. The Moving Man

53. Analyzing Graphs Using slope and area of Δ V vs. t graphs to determine Δ X vs. t and a vs. t graphs

54. Analyzing Graphs Using slope and area of Δ V vs. t graphs to determine Δ X vs. t and a vs. t graphs

55. Analyzing Graphs Using slope and area of Δ V vs. t graphs to determine Δ X vs. t and a vs. t graphs Velocity (m/s) 20 15 10 5

56. Analyzing Graphs Using slope and area of Δ V vs. t graphs to determine Δ X vs. t and a vs. t graphs Velocity (m/s) 20 15 10 5

57. Analyzing Graphs Using slope and area of Δ X vs. t graphs to determine Δ V vs. t and a vs. t graphs

58. Analyzing Graphs Using slope and area of Δ V vs. t graphs to determine Δ X vs. t and a vs. t graphs

59. Analyzing Graphs Using slope and area of Δ V vs. t graphs to determine Δ X vs. t and a vs. t graphs

60. Analyzing Graphs Using slope and area of Δ V vs. t graphs to determine Δ X vs. t and a vs. t graphs