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# Relative Motion

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1. Relative Motion

2. Frames of Reference • Object or point from which motion is determined • Most common is the earth • Motion is a change in positionrelative to a frame of reference

3. What is motion? • If you are standing in one place, and your friend walks by you, are you moving relative to your friend? • Is your friend moving relative to you? • Is either of you moving relative to the earth?

4. Answer: • You are moving relative to your friend, and your friend is moving relative to you! • You are not moving relative to the earth, but your friend is. You are both moving relative to the sun!

5. What is motion? • If you and your friend are walking down the hall together at the same speed, in the same direction, are you moving relative to your friend? • Is your friend moving relative to you? • Are either of you moving relative to the earth?

6. Answer: • You are NOT moving relative to your friend, and your friend is NOT moving relative to you. You both are moving relative to the earth.

7. Uniform motion Uniform motion – occurs when an object is moving at a constant speed/ velocity in a straight line. Constant speed/velocity- means that the object is covering the same distance per unit of time. Scalar – any quantity that is represented by a magnitude and a unit. Vector – any quantity that is represented by a Magnitude, a unit and a direction.

8. Distance and Displacement • Distance(d) is a scalar measure of the actual path between two locations . • It has a magnitude and a unit. • Ex: 50 m, 2.5 hrs. • Displacement(d) is a vector measure of the change in position measured in a straight line from a starting reference point. • Ex: 5 m [W]

9. Sign Convention • In physics we will use a standard set of signs and directions. • Up, right, east and north are positive directions. ( + ) • Down, left, west, and south are negative directions. ( - )

10. Distance – total trip d total = d1 + d2 + d3 + d4 d total = 2m + 4m + 2m+ 4m d total = 20 m Displacement – change in position d total = +d1 + +d2 + -d3 + -d4 d total = +2m + +4m + -2m+ -4m d total = 0 m

11. Speed • Speed = Change in distance ÷ Time Δ d_ V T Example: A car travels 300km in 6 hours. What is the speed of the car?

12. Answer: • Speed = distance ÷ time • Speed = 300km ÷ 6 hours • Speed = 50km/hr

13. More practice • 1. How far can a plane travel if it flies 800km/hr for 9 hours? • 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr?

14. Answer 1. Δ d V T Δ d 800 9 800km ▪ 9hrs = 7200km hr

15. Answer 2. Δ d V T 500 50 T 500km ÷ 50km = 10 hrs hr

16. Instantaneous Speed • Instantaneous speed is speed at any instant in time. • A speedometer measures speed in ‘real time’ (the instantaneous speed).

17. Average Speed • Average speed is the average of all instantaneous speeds; found simply by a total distance/total time ratio • The average speed of a trip: Vavg = d1 + d2 + d3 + d4........ t1 + t2 + t3 + t4 ..........

18. Velocity • Speed in a given direction is velocity ( vector). • What is the velocity of a boat that travels from St. John’s, west to Longpond • (16 Km ) in 2.5 h ?

19. Answer • Velocity = displacement ÷ time • Velocity = 16 Km ÷ 2.5 h • Velocity = 6.4 km/h • Velocity = 6.4 km/h west

20. Change your answer to m/s! • = 6.4 km/h ÷ 3.6 = 1.8 m/s Km/hr to m/s conversion trick Km/hr m/s m/s K/hr Divide by 3.6 multiply by 3.6

21. Difference Between Speed and Velocity Scalar Quantities ( Number and unit) Vector Quantities ( Number, unit and direction) 10 Km West 50 Km/hr south 100 newtons right Velocity (Speed and Direction) Volume liters Distance Voltage Speed (KM/h) Speed is a Scalar Quantity Velocity is a Vector Quantity

22. Distance-time graphs • On your paper, graph the following: • D (m) T (sec) 0 0 5 7 10 14 15 21

23. Distance (m) time (sec)

24. Was your graph a straight line? • A distance-time graph which is a straight line indicates constant speed. • In constant speed, the object does not speed up or slow down. The acceleration is zero.

25. The Steeper the slope the faster the object is moving.

26. y2 y1 x1 x2 On a distance time graph for uniform motion the slope equals the average speed. Vavg =Δd Δt

27. What is the Vavg for this graph? 8 - 4 = 4 = 2m/s 4 – 2 2

28. Displacement Time Graphs • Like distance time graphs only displacement can be either positive or negative, therefore we need two quadrants. d d d d t t t t Stopped right of origin Stopped left of origin Moving left away from origin Moving right toward origin from left

29. d B A t C Graphing ! A … Starts at home (origin) and goes right (+) slowly B … Stopped (position remains constant as time progresses) C … Turns around and goes in the (-) direction quickly, passing by home

30. Explain what is happening for each leg of the trip.

31. Explain what is happening for each leg of the trip. What is the velocity for each leg of the trip? Hint: slope= rise/ run = Δ d = d2 – d1 = Avg. velocity t t2 – t1

32. Graph the following on a distance-time graph: • d (m) t (s) 0 0 5 1 20 2 45 3 80 4 125 5

33. Distance (m) 0 1 2 3 4 5 time (sec)

34. Was your graph a curve? • A graph that curves on a distance-time graph shows that the object is accelerating ( non-uniform motion). • Acceleration.

35. Distance-time graphs • Describe the motion of the object as shown in the graph. From 0-8 sec, constant speed: (25 m/sec); From 8-12 sec, no motion (stop); From 12-16 sec, acceleration; From 16-20 sec, constant speed

36. Speed-time graphs • Using the distance-time graph from the last frame, draw a speed time graph. First fill in the table below: Average Speed (m/s) Time (sec) ____ 0 to 8 ____ 8 to 12 ____ 12 to 20 25 0 37.5 Draw on board

37. What does your graph look like? • Constant speed will be a horizontal line on a speed time graph. • If the speed decreases, the line will slant down. • If the speed increases, the line will slant up.

38. On a velocity - time graph the area between the graphed line and the x-axis equals the displacement Area = l x w = 6 s x 30 m/s = 180 m

39. This object is slowing down in a positive direction. It is non-uniform motion. However we can still calculate the displacement by finding the area of the triangle. ( ½ base x height ) Displacement = ½ base x height = ½ 25.0 m/s x 25.0 s = 312.5 m Note how the units cancel.

40. Object is moving at a constant speed for 5.0 s then it speeds up for the next 5.0 sec. Displacement = area of rectangle + area of a triangle = l x w + ½ base x height = 10.0 s x 5.0m/s + ½ 10.0 m/s x 5.0 s = 50 m + 25 m = 75m

41. Object moving right and speeding up. (+) Object moving left and speeding up. (-) Object moving right and slowing down. (+) Object moving left and slowing down (-)

42. The slope of the line on a velocity time graph equals the average acceleration. For uniform motion the graph is horizontal, therefore the slope is zero and the acceleration is zero.

43. d Graphing w/ Acceleration C B t A D A … Start from rest south of home; increase speed gradually B … Pass home; gradually slow to a stop (still moving north) C … Turn around; gradually speed back up again heading south D … Continue heading south; gradually slow to a stop near the starting point

44. d Tangent Lines t On a position vs. time graph: The slope of a tangent line will give the velocity at that point in time. ( instantaneous velocity )

45. v t a t Graphing Tips The same rules apply in making an acceleration graph from a velocity graph. Just graph the slopes! Note: a positive constant slope in blue means a positive constant green segment. The steeper the blue slope, the farther the green segment is from the time axis.

46. d t Area under a velocity graph “forward area” “backward area” Area above the time axis = forward (positive) displacement. Area below the time axis = backward (negative) displacement. Net area (above - below) = net displacement. Total area (above + below) = total distance traveled.

47. d t All 3 Graphs v t a t

48. What do the following speed-time graphs depict?

49. Acceleration • Change in velocity • Can be change in speed or direction • Acceleration = ∆V/ ∆T • ∆V a t