1. Click here to enter

2. Click a menu option to view more details Starters Main Courses Desserts Click on the coffee cup to return when Navigating For Vocabulary Subject Related Content and tutorials For drill and practice applet

3. Please make your choice from the following selections Click on the documents below to see Essential vocabulary for Kinematics

4. Please make your choice from the following selections Solving Kinematics Problems Reading kinematics Graphs Vectors

5. Please make your choice from the following selections Kinematics Graph Applet Finding Vector Components Applet Type 1 Projectile Problem

6. Constant Velocity Motion Constant Acceleration Motion

7. Position versus time Velocity versus time

8. Click the above icon to access the Kinematics Graph Applet

9. Click here for Kinematics Problems Click here for Free-Fall Problems

10. 1. To begin click the ‘problem’ button 2. When finished, hit ‘solution’ to see the answer 3. Hit ‘problem’ again to get a new problem 4. Hit the coffee cup to return to the previous menu ProblemSolution Vector 11m @ 80 Degrees South of West Horizontal Component Vertical Component

11. Constant Velocity

12. Position versus time 1. The slope of the Position versus time graph is the velocity of the object 2. The y-intercept is the initial position

13. Position versus time 1. Since this graph has a constant positive slope, it has a constant positive velocity and zero acceleration 2. All objects with linear Position versus time graphs have no acceleration !!!

14. Position versus time 1. So its velocity versus time graph would look like this. 2. Observe that the value of its velocity does not change, it is always the same positive value and the slope of the previous graph

15. Position versus time This Position versus time graph has a constant negative slope. That means it has a constant negative velocity and its velocity versus time graph would look like this:

16. Constant Velocity Position versus Time Graph Click here to repeat the tutorial Click here to return to the Constant Velocity Kinematics Graph Tutorial Menu Or click the mug to return to the main menu

17. Constant Acceleration

18. Velocity versus time 1. The slope of the velocity versus time graph is the acceleration of the object 2. For constant velocity, the slope will always be zero 3. The y-intercept is the initial velocity.

19. Velocity versus time 1. This velocity versus time graph has a constant value of 20m/s for all values of time. 2. This means that the slope of a position versus time graph for the motion of this object is 20m/s

20. Velocity versus time 1. This velocity versus time graph has a constant value of 20m/s for all values of time. 2. This means that the slope of a position versus time graph for the motion of this object is 20m/s 3. The position versus time graph for this velocity versus time graph would look like this

21. Velocity versus time 1. This velocity versus time graph has a constant value of 20m/s for all values of time. 2. This means that the slope of a position versus time graph for the motion of this object is 20m/s 3. The position versus time graph for this velocity versus time graph would look like this

22. Velocity versus time What would the position versus time graph look like for this velocity versus time graph? Click here for answer.

23. Velocity versus time What would the position versus time graph look like for this velocity versus time graph? Click here for answer.

24. Constant Velocity Velocity versus Time Graph Click here to repeat the tutorial Click here to return to the Constant Velocity Kinematics Graph Tutorial Menu Or click the mug to return to the main menu

25. Position versus time Velocity versus time Acceleration versus time

26. Constant Acceleration

27. Position versus time 1. For an object that is accelerating, the graph will be quadratic 2. An upward inflection means a positive acceleration 3. A downward inflection means a negative acceleration

28. Position versus time Speeding Up Both of these graphs show objects that are speeding up. Observe that the graph shows a line such that the slope is constantly increasing over time

29. Position versus time Slowing Down Both of these graphs show objects that are slowing down. Observe that the graph shows a line such that the slope is approaching zero with increasing time

30. Position versus time Velocity Versus time This position versus time graph show an object going from zero velocity(no slope) to some positive velocity. Therefore its velocity versus time graph is linear with a positive slope and the initial velocity is zero.

31. Position versus time Velocity Versus time This position versus time graph show an object going from zero velocity(no slope) to some negative velocity. Therefore its velocity versus time graph is linear with a negative slope and the initial velocity is zero.

32. Position versus time Velocity Versus time This position versus time graph show an object going from some positive velocity to zero velocity(no slope). Therefore its velocity versus time graph is linear with a negative slope and the initial velocity is some positive value.

33. Position versus time Velocity Versus time This position versus time graph show an object going from some negative velocity to zero velocity(no slope). Therefore its velocity versus time graph is linear with a positive slope and the initial velocity is some negative value.

34. Constant Acceleration Position versus Time Graph Click here to repeat the tutorial Click here to return to the Constant Acceleration Kinematics Graph Tutorial Menu Or click the mug to return to the main menu

35. Constant Velocity

36. Velocity versus time 1. The slope of the velocity versus time graph is the acceleration of the object. 2. The y-intercept is the initial velocity.

37. Velocity versus time Speeding Up Both of these velocity versus time graphs are for objects that are speeding up. Observe how both graphs get further from zero velocity with time.

38. Velocity versus time Slowing Down Both of these velocity versus time graphs are for objects that are slowing down. Observe how both graphs approach zero velocity with time.

39. Velocity versus time This velocity versus time graph has a slope of 10m/s 2 Its acceleration versus time graph would look like this: This is the same relationship that Constant Velocity Position versus time graphs have to velocity versus time graphs

40. Velocity versus time This velocity versus time graph has a slope of 10m/s 2 Its position versus time graph would look like this: Observe how the position versus time graph gets steeper with time. Remember that the steepness relates to the velocity.

41. Velocity versus time What would the position versus time and acceleration versus time graphs look like for this velocity versus time graph? Click here for the answers

42. Velocity versus time What would the position versus time and acceleration versus time graphs look like for this velocity versus time graph? Click here for the answers

43. Velocity versus time This velocity versus time graph has a slope of -10m/s 2 and a y-intercept of 45m/s Its acceleration versus time graph would look like this: This is the same relationship that Constant Velocity Position versus time graphs have to velocity versus time graphs

44. Velocity versus time This velocity versus time graph has a slope of -10m/s 2 and a y-intercept of 45m/s Its position versus time graph would look like this: Observe how the position versus time graph gets less steeper with time. Remember that the steepness relates to the velocity.

45. Velocity versus time What would the position versus time and acceleration versus time graphs look like for this velocity versus time graph? Click here for the answers

46. Velocity versus time What would the position versus time and acceleration versus time graphs look like for this velocity versus time graph? Click here for the answers

47. Velocity versus time Observe that both of these velocity time graphs have the same acceleration versus time graph Speeding Up Slowing Down Whether an object speeds up or slows down does not depend on the direction of the acceleration

48. Velocity versus time Observe that both of these velocity time graphs have the same acceleration versus time graph Speeding Up Slowing Down But rather whether or not the velocity and acceleration vectors agree on direction. Remember the sign of a vector(+ or -) indicates direction.

49. Constant Acceleration Velocity versus Time Graph Either click here to repeat the tutorial or click the mug and return to the main menu Click here to return to the Constant Acceleration Kinematics Graph Tutorial Menu Or click the mug to return to the main menu

50. Finding vector components Adding Vectors

51. How to graphically find components

52. First draw a coordinate system

53. Then draw your vector coming out of the origin. 5m @ 45 degrees East of North

54. To draw the horizontal component, start at the origin and draw a vector arrow out until you are directly below the arrow head of your vector Horizontal Component ‘x’ 5m @ 45 degrees East of North

55. To draw the vertical component, start at the head of the horizontal vector and the draw a line to the head of the original vector Horizontal Component ‘x’ Vertical Component ‘y’ 5m @ 45 degrees East of North

56. Take note that you get the same answer if you start with the vertical component first. 5m @ 45 degrees East of North Same Length!!!

59. Standard Kinematics Solving Kinematics Problems

60. Solving Standard Kinematics Problems Problem Solving steps 1. Read the problem 2. Identify the type of motion 3. Make your list of kinematics variables based on the type of motion. 4. Determine what you are asked to find. 5. Determine what information you are given 6. Choose an equation based on what you know and what you are looking for. 7. Solve. Remember to label your answer with proper units.

61. Solving Standard Kinematics Problems When solving standard kinematics problems it is important to identify what type of motion the object in the problem is exhibiting. The variables and equations you use to solve the problem are dependent on identifying this correctly. Using a constant velocity equation to find information about an object that is accelerating will yield a wrong answer.

62. Solving Standard Kinematics Problems Types of Motion Constant VelocityConstant Acceleration For constant velocity motion use the variable list on the left For constant acceleration motion, use the variables list on the right

63. Solving Standard Kinematics Problems Types of Motion Constant VelocityConstant Acceleration For constant velocity motion you must use the equation on the left For constant acceleration motion, you must use one of the equations on the right

64. Solving Standard Kinematics Problems Units Distance Displacement Position m Speed Velocity m/s Acceleration m/s 2 Units are important because they tell you what a number is. It is very useful to learn what units go with what variable

65. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Step 1 Read the problem

66. Step 2 Identify the type of motion Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? This object is accelerating. I know this because it asks for the acceleration. When determining the type of motion, look for reference clues. Ask yourself, “Is the object changing speed or traveling at a constant one?” Starting from rest and stopping are signs of acceleration.

67. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Step 3 Make your list of variables Since this object is accelerating I will use my list of variables for constant acceleration motion

68. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Step 4 Determine what you are looking for This problem asks for acceleration. Since it is directly asking what the acceleration is I must be looking for acceleration. Put a box around this variable to remind yourself it is what you are looking for.

69. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Step 5 Determine what information you are given An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? This problem mention a velocity of 71m/s is needed for take off. I know this is the final velocity because the plane will be leaving the ground at the end of the problem, not the beginning.

70. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? This problem mention a runway length of 1.0km. This means that the plane will have a displacement of 1.0km after taking off because it will have traveled 1.0km from its starting point when it reaches its take off position. Because of this, its final position would be 1.0km and the initial position would be 0m. I can always assume an initial position of 0m if none is mentioned.

71. Solving Standard Kinematics Problems Example Since the plane is taking off, it starts from rest. Be aware of reference clues. Key phrases to look for with velocity information are starts from rest, comes to a stop, etc. Look for this as well. An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be?

72. Solving Standard Kinematics Problems Example Remember 1km=1000m Use this fact to convert this to m Check to make sure all of the units in your table match. If not, make any necessary conversions An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? This is in km and the rest are all m. This needs to be converted to m to match the other units

73. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Step 6 Choose an equation Since this is constant acceleration motion, I must pick from the constant acceleration equations.

74. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Choose your equation based on what you know and what you are looking for

75. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? This equation has what I am looking for and I know all of the other variables that appear in it.

76. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Step 7 Solve Plug in what you know and solve.

77. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Square the 71m/s

78. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Eliminate the zero terms

79. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Multiply the 1000m by 2

80. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Divide both sides by 2000m

81. Solving Standard Kinematics Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Rearrange so that the a appear on the left.

82. Solving Standard Kinematics Problems Click here to repeat the tutorial Click here to return Solving Kinematics Problem Menu Or click the mug to return to the main menu

83. Free-Fall Problems Solving Kinematics Problems

84. Solving Free-Fall Problems To solve a free-fall problem, you use the same steps as a standard kinematics problem To Review, the steps are as follows: 1. Read the problem 2. Identify the type of motion 3. Make your list of kinematics variables based on the type of motion. 4. Determine what you are asked to find. 5. Determine what information you are given 6. Choose an equation based on what you know and what you are looking for. 7. Solve Remember to label your answer with proper units.

85. Solving Free-Fall Problems The only difference with a free fall problem in problem solving is is that the type of motion is always constant acceleration and the value of the constant acceleration is always 9.8m/s 2 This concept is labeled g in physics and the value of g is always 9.8 m/s 2

86. Solving Free-Fall Problems When identifying free-fall problems, look for objects being dropped. Also included are objects that are thrown up or thrown down. These are also free falling objects. As we will see later, free-fall is a special case of projectile motion. A projectile is an object that is travelling through the air and only subject to the force of gravity. A free-falling object is a projectile with only a vertical motion.

87. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Step 1 Read the problem

88. Step 2 Identify the type of motion Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? This is a free fall problem. I know this because the object has been dropped. This means that it is a special case of constant acceleration motion.

89. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Step 3 Make your list of variables Since this object is free-falling, I will use my list of variables for constant acceleration motion

90. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Step 4 Determine what you are looking for This problem is asking for two things. First how fast is it traveling just before impact. That would be the final velocity. Also, it asks what height it was dropped from, that would be the initial position. A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from?

91. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Step 5 Determine what information you are given A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? The problem mentions it takes 1.5s to reach the ground. Therefore the time is 1.5s

92. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? I also know that the ball is about to reach the floor at the end of the problem. This would be zero position. So the final position of the ball is 0m

93. Solving Free-Fall Problems Example I also know that this ball has been dropped. Anything that is dropped has an initial velocity of zero since after first letting go it is not moving. A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from?

94. Solving Free-Fall Problems Example It may appear at first sight that this problem does not have enough information to solve. Most free-fall problems appear this way. But for a free-fall problem I always know that the value of a=g. So a is -9.8m/s 2. It is negative because the direction of the acceleration is down. A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from?

95. Solving Free-Fall Problems Example Check to make sure all of the units in your table match. If not, make any necessary conversions A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? In this case we are ok because they all match

96. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Step 6 Choose an equation Since this is free fall motion, I must pick from the constant acceleration equations.

97. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Choose your equation based on what you know and what you are looking for. In this case I am looking for two things and it does not matter which I do first. I will start with solving for the final velocity.

98. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? This equation has what I am looking for and I know all of the other variables that appear in it.

99. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Step 7 Solve Plug in what you know and solve.

100. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Eliminate the zero terms

101. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Multiply the -9.8m/s 2 by the 1.5s This negative answer makes sense. Remember with vectors, signs indicate direction and this object is traveling down.

102. Solving Free-Fall Problems Click here to repeat the tutorial for solving for the final velocity Click here to proceed to the tutorial for solving for height of release

103. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Now we will solve for the height of release. Again we will use our equations for constant acceleration and we can keep our variable list from the previous problem.

104. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? This equation has what I am looking for and I know all of the other variables that appear in it.

105. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Plug in what you know and solve.

106. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Multiply the ½ by the -9.8m/s 2 and the 1.5 2 s

107. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Eliminate the zero terms

108. Solving Free-Fall Problems Example A ball is dropped and it takes 1.5s to reach the floor. How fast is it traveling right before impact and how high above the floor was it dropped from? Add 11m to both sides

109. Solving Free-Fall Problems Example An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? Rearrange so that the x 0 appear on the left.

110. Solving Kinematics Problems Standard Kinematics Click here to repeat the tutorial Click here to return Solving Kinematics Problem Menu Or click the mug to return to the main menu

111. 1. To begin click the ‘problem’ button 2. When finished, hit ‘solution’ to see the answer 3. Hit ‘problem’ again to get a new problem 4. Hit the coffee cup to return to the previous menu Toggle show the components motion Toggle show the resultant Motion A ball traveling 14 m/s rolls off a cliff and lands 100m away from the base of the cliff. Determine the time of fall and the height of the cliff. Vo=14 m/s ? 100m Answer Time of Fall= 7.14 s Height= 249.8 m Problem