1. CHAPTERS 3 & 4 • 3.1 Picturing Motion • Motion Diagrams • A series of consecutive frames (frame by frame) of the motion of an object. Similar to movie film (30 frames per second).

4. The Particle Model • Motion diagram of wheel with two different dots, center of wheel and edge of wheel.

5. 3.2 Where & When? • Coordinate Systems • 2 dimensional • AKA x-y coordinate system

6. Vectors and Scalars • Scalar Quantity= • A quantity that tells you only the magnitude (size/amount) of something. • A number with units. • Examples: • 42kg, 100oC, 40s, 10hr, $89, 100m/s,

7. Vector Quantity • Vector Quantity= • Magnitude with direction. • Example: • 46km/hr North, 15m/s SW, 58km→ • Vectors are drawn to scale, the larger the vector, the larger the magnitude. • Examples on board.

8. Vectors

9. Time Intervals and Displacement • Displacement (Δd) = • The distance and direction between two positions. • Δd = df – di • df = final position • di = initial position • Δd can be positive/negative • Examples on number line.

10. Time Interval (Δt) = • The time required for an object to complete some displacement. • Δt = tf – ti • tf = final time • ti = initial time (usually ti = 0) •  Δt is always positive

11. 3.3 Velocity and Acceleration • Velocity • Speed vs velocity, is there a difference or are the terms interchangeable? • Speed examples: • 57m/s, 37km/hr, 17cm/yr, 68mph •  speed is a scalar quantity.

12. Velocity = • Speed with direction, a vector quantity. • Examples: • 57ms East, 37km/hr SE, 17 cm/yr→, 68mph West

13. 67m/s @ 300o

14. 75m/s @ 38o N of W

15. Average velocity _ Δddf - di • Avg vel (v)= Δt = tf – ti ________ • avg vel = vector quantity (speed&direction) • Examples on number line.

16. The frog jumps from 0m to 9m in 3 seconds, what is the frog’s avg vel?

17. Δddf – di • avg vel = Δt = tf – ti = • 9m – 0m9m • 3s – 0s = 3s = 3m/s

18. Other Examples • 1. A runner begins at the starting line and crosses the 80m finish line in 4 seconds. What is the runner’s average velocity? • A = 20m/s • 2. A car travels from the school, 200km West in 5hr. What is the car’s average velocity? • A = -40km/hr

19. Instantaneous Velocity = ? • The speed and direction of an object at a particular “instant” in time, how fast it is moving right now. • Examples of instantaneous velocity = • Speedometer, radar gun, tachometer

20. Motion Diagram of Golf Ball • Examples on Board: • Golf putting right/left (+v, -v, )

21. EQUATIONS • V = vi + at v = vel (inst/final) vi = initial velocity • V2 = vi2 + 2aΔd Δd = df - di • df = di + vΔt

22. Acceleration (a) = • The rate of change in velocity (Δv). Δvvf - vi • a = Δt = tf - ti • Example: A car pulls out from a stop sign, 20s later it is traveling West at 40m/s. What is the car’s acceleration.

23. Δvvf - vi -40m/s - 0m/s • a = Δt = tf - ti = 20s - 0s -40m/s • a = 20s = -2m/s2

24. Examples of acceleration Motion Diagrams • Car speeding up, then constant velocity, then slowing down.

25. All problems all year for every chapter MUST have the following or points will be deducted. HOMEWORK INCLUDED! • 1. A sketch/drawing or FBD. • 2. Table of Known/unknown values. • 3. Write the equation(s) to be used. • 4. Plug in numbers • 5. Show ALL steps/work.

26. More Equations • vf2 = vi2 + 2aΔd • vf2 = vi2 + 2a(df - di)

27. 4.1 Properties of Vectors • Graphical representation = • An arrow is drawn to scale and at the proper direction. • The length of the arrow represents the magnitude of the vector.

28. VECTOR EXAMPLES

29. Resultant Vector (R) = • The sum of 2 or more vectors. • R = vector 1 + vector 2 + vector 3 +…

30. Resultant Vector Example • Examples on board • 1. 2 equal vectors • 2. 2 equal/opposite vectors • 3. 2 vectors 90o apart

31. Resultant Vector Example

32. Resultant Vector Example • From SVHS to home various examples. • No matter which route you take the displacement (Δd) will be the same.

33. Graphical Addition of Vectors • Vectors are drawn from tip to tail

34. Resultant Vector (R) = • The sum of two or more vectors. • The order of adding the vectors does not matter, just like adding any other values. • Since the vectors are drawn to scale, the magnitude of the resultant ( R ) can be measured with a ruler.

35. Resultant Vector Example

36. Resultant Vector Example

37. Resultant Vector Example • Example on board: • 2 different paths – use meter stick • The resultant vectors (R), are equal, the path does not matter, when all the individual vectors are added together the resultants will be equal.

38. What is the magnitude of R for the vectors below?

39. What is the magnitude of the R vector below?

40. What is the magnitude of the vectors below? The red vector has a magnitude of 40, the purple vector 65, use the indicated angles.

41. Can you use the Pythagorean Theorem? • NO! • Why not? • Because the triangle is NOT a right triangle. • How can you solve for the resultant? • You must use the LAW of Cosines.

42. Law of Cosines Equation • R2 =A2 + B2 - 2ABcos • R2 = 402 + 652 – 2(40)(65)(cos119o) • R2 = 1600 + 4225 – 5200(-0.48409) • R2 = 5825 + 2517.27 • R2 = 8342.27 • R = √¯8342.27 • R = 91.37

43. Relative Velocities: Some Applications • You are in a bus traveling at a velocity of 8m/s East. You walk towards the front of the bus at 3m/s, what is your velocity relative to the street? • 11m/s

44. You are in a bus traveling at a velocity of 8m/s East. You walk towards the back of the bus at 3m/s, what is your velocity relative to the street? • 5m/s

46. A plane is traveling North at 800km/h, the wind is blowing East at 150km/h. What is the speed of the plane relative to the ground? • 1. Draw sketch of vectors • 2. List known/unknown • 3. Write equation • 4. Plug in numbers • 5. Solve showing all work/steps

47. Solve Example • Use Pythagorean Theorem A2 + B2 = C2 • Vpg2 = Vp2 + Vw2 • Vpg = √¯Vp2 + Vw2 • Vpg = √¯(800km/h)2 + (150km/h)2 • Vpg = √¯640,000km2/h2 + 22,500km2/h2 • Vpg = √¯662,500km2/h2 • Vpg = 813.9km/h

48. Boat/River Example • A river flows South at 8m/s, a boat travels due East at 15m/s. Where will the boat end up and what will the boat’s speed be relative to the shore? • 1. Draw sketch of vectors • 2. List known/unknown • 3. Write equation • 4. Plug in numbers • 5. Solve showing all work/steps

49. C2 = A2 + B2 • R2 = VB2 + VR2 • VBS2 = VB2 + VR2 • VBS2 = (15m/s)2 + (8m/s)2 • VBS = √¯(225m2/s2) + (64m2/s2) • VBS = √¯289m2/s2 • VBS = 17m/s

50. 4.2 Components of Vectors • Choosing a Coordinate System