1. LINEAR MOTION Chapter 2

2. Motion Everywhere – people, cars, stars, cells, electricity, electrons Rate = Quantity/time How fast something happens

3. Linear Motion Motion on a straight path Scalar- Distance and speed Vector – Displacement and velocity

5. Motion is Relative Everything moves Things that seem at rest are moving in relation to stars and sun  Book on a desk moves at 30 km/sec in relation to the sun  Same book is even faster in the galaxy In this chapter – we look at motion compared to earth

8. Speeds Snail - 2 meters/day Indy racecar – 300 km/hr Space shuttle – 8 km/sec

9. Speed Distance / time “per” – divided by – “/” Any combination of units is useful depending on situation Km/hr, cm/day, light-years/hour Most common – m/sec and mile/hr

10. Average Speed Total distance/time interval Examples: 60 km in 1 hour = 60 km/hr 240 km in 4 hour = 60 km/hr  Note the units Does not indicate all the stops and starts

12. The longer the time period measured, the more it leads to calculating an average velocity. The longer the time period measured, the more it leads to calculating an average velocity. The shorter the time period measured the closer it brings you to calculating an "instantaneous velocity". Only if the time period The shorter the time period measured the closer it brings you to calculating an "instantaneous velocity". Only if the time period The longer the time period measured, the more it leads to calculating an average velocity.

13. Constant Speed If the speed does not change over a long period, it is like Average speed Length = velocity x time l = v con t

14. Instantaneous Speed Speed at any moment Speed can vary with time Speedometer – measures instantaneous speed

15. The shorter the time period measured the closer it brings you to calculating an "instantaneous velocity". Only if the time period becomes zero would we truly have an instantaneous velocity.

16. Refer the adjoining figure and calculate the distance between the two signals? Insert graph Question 2 Chapter 2 Chapter Assessment Questions A. 3 m B. 8 m C. 5 m D. 5 cm

17. Chapter Assessment Questions Answer: C Answer 2 Chapter 2 Reason: Distance  d = d f – d i Here, d f = 8 m and d i = 3 m Therefore,  d = 8 m  3 m = 5 m

18. Questions The speedometer in every car also has an odometer that records distance: If the odometer reads zero at the beginning of the trip and 35 km a half-hour later, what is the average speed? Would it be possible to attain this average speed and never exceed 70 km/hr? If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In one minute?

19. Graph of Constant speed Average speed is the slope of the line during an interval If it is a curve, the instantaneous speed is the line tangent to the curve at that point

20. Delta Notation Δ – Greek capital letter – Delta Signifies a change in a quantity Δ l = l f – l i Δ t = t f -t i v = Δ l = l f – l i Δ t t f - t i

21. Velocity EDL (every day life) – speed and velocity are interchangeable Physics – Velocity – speed in a direction 60 km/hr North Question – The speedometer of a car moving northward reads 60 km/hr. It passes another car that travels southward at 60 km/h. Do both cars have the same speed? Do they have the same velocity?

22. Constant Velocity Constant speed and direction Must move in a straight line Curves change the direction Changing velocity- in a car there are 3 things to change velocity – Gas Brakes Steering wheel

24. The Displacement Vector Displacement is the straight-line shift in position from P o to P f Included length and direction Vector Magnitude Direction

25. Resultant The vector that is drawn between two points

26. Vector Algebra Rules for dealing with vectors Helps us understand how to manipulate them

27. Tip-to-Tail Method Add vectors by placing tip of one to the tail of the other. The resultant is from the tail of one to the tip of another

28. Tip-to-Tail Method Order of addition is irrelevant

29. Parallelogram Method Use 2 set vectors to make a parallelogram The diagonal is the resultant

30. Multiple Vectors Add more than 2 vectors by the tip-to- tail method

31. Parallel Vectors Parallel – Simple sum Anti-parallel (opposite directions) - Difference

32. Acceleration How fast is velocity changing Acceleration is a RATE (of a rate) Change in velocity Acceleration Deceleration Change in direction Acceleration = Change in velocity/time

34. Question Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 45 km/h, then 45 to 50 km/h. What is its acceleration? In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. Which undergoes greater acceleration? What is the acceleration of each vehicle?

35. Average Acceleration a – acceleration (m/s^2) v – velocity (m/s) t – time (s)

36. Average acceleration problem Problem – What is the acceleration of a car the screeches to a stop from 96.54 km/h in 3.7 seconds?

38. Instantaneous Acceleration Velocity vs. Time graph Slope of line tangent is equal to ACCELERATION Sign of Slope  Positive – accelerating  Negative - decelerating

39. Velocity-Time Graph of Accelerating Car Tangent Slope = acceleration velocity time

40. Uniform accelerated motion In the real world, acceleration is seldom constant In problems, we can consider it constant for a few moments Motion is in a straight line V f – final velocity V i – initial velocity

41. Uniform accelerated motion v f = v i + at Problem – What is the final speed of a bicyclist moving at 25.0 km/h who accelerates +3.00 m/s^2 for 3.00 sec?

42. The Mean Speed What is v av for an object that is uniformly accelerating from v i to v f ? Mean speed = v av = ½ ( v i + v f )

43. Area under the Graph Equals the total distance moved Area of a retangle = m/s x s = Meters

44. More complex Area under still equals distance

45. Mean Speed Theorem s = ½ ( v i + v f ) t Problem- A bullet is fired with a muzzle speed of 330m/s down a 15.2 cm barrel. How long does it take to travel down the barrel?

46. Constant Acceleration Equations THE BIG FIVE v f = v i + at v av = ½ ( v i + v f ) s = ½ ( v i + v f ) t s = v i t + ½ at² v f ² = v i ² + 2as

47. When v f is unknown One sports car can travel 100.0 ft in 3.30 seconds from 0m/s. What is the acceleration?

48. When t is unknown Problem – What is the cheetah’s acceleration if it goes 0 to 72 km/hr in 2.0 seconds? - How far will it go to be moving 17.9 m/s?

49. Freefall – How Fast An apple gains speed as it falls Gravity causes acceleration EDL – air resistance effects freefall acceleration

50. Freefall Elapsed Time Instant. Speed (m/sec)0 110 220 330 440 t10t

51. Freefall Acceleration = change in speed time = 10 m/s/s = m/s 2 Unit – meter/second/second speedtime interval Equations : a = V instantaneous /t V instantaneous = at

52. Gravity acceleration g = acceleration due to gravity Actually measures 9.81 m/ s 2 In English – 32 ft/sec² Speed instantaneous = acceleration x time v instantaneous = gt

53. Question What would the speedometer reading on the falling rock be 4.5 seconds after it drops from rest? How about 8 seconds after it is dropped? 15 seconds?

54. What about an object thrown upward? On the way up it decelerates 9.81m/ s 2 On the way down it accelerates 9.81m/ s 2

55. Free Fall – How Far? Fast and far are different At the end of 1 sec the speed is 9.81m/ s 2 Did it travel 9.81 m?  NO – it was accelerating from 0 m/ s 0 m/s  9.81 m/s  Average speed = 4.90 m/s

56. Question During the span of fall, the rock begins at 10 m/s and ends at 20 m/s. What is the average speed during this 1-second interval. What is its acceleration?

57. Distance in gravity Mathematical pattern for the distance something falls in time: distance = ½ gravity x time 2 d= ½ gt 2

58. Questions An apple falls from a tree and hits the ground in one second. What is the speed upon striking the ground? What is its average speed during the one second? How high about ground was the apple when it first dropped?

59. Graphs of Motion Velocity vs. Time- freefall Linear - directly proportional Slope is constant = acceleration Velocity Time

60. Graphs of Motion Distance vs. Time Parabolic Slope is variable = Speed Distance Time

61. Air resistance Effects feathers and paper Not much effect on things with low profiles

62. How fast, far, and quickly Don’t mix up fast and far Acceleration – rate of a rate Rate at which velocity changes Be patient – it took 2000 years from Aristotle to Galileo to straighten it all out!!