Chapter One

Lesson One

  1. Describing Position
  2. Think for a moment…..
  3. How would you describe where you are right now?
  4. Would it be based on who is to the left of you or to the right of you?
  5. How would you describe where to meet up if you wanted to meet up with your friends?
  6. What do all these questions refer to?
  7. Using a reference point to describe a position
  8. No matter how you describe such positions, they all have one common factor and that is that they all state your location relative to a certain point.
  9. This point is known as a reference point.
  10. Reference point
  11. The starting point you choose to describe the location or position of an object
  12. Each description includes the distance and direction from the reference point.
  13. Such descriptions of your location helps in defining your position.
  14. Position
  15. An object’s distance and direction from a reference point
  16. Changing the reference point
  17. The description of an object’s position depends on the reference point
  18. Example:
  19. How you describe your position from SMART Board at the front of the classroom?
  20. The reference direction
  21. When describing an object’s position, you typically compare its location to a reference direction.
  22. In other words, you are looking at the direction in which you are going away from the reference point.
  23. Typically uses positive or negative references when describing direction.
  24. Positive can typically represent what is to the right of the reference point, while negative can typically represent what is to the left of the reference point.
  25. In other words, think of it like a number line. If you were to start at 0 and go towards 1, then you are going in a positive direction (right). If you were to start at 0 and go towards -1, then you are going in a negative direction (left).
  26. Describing Position in Two Dimensions
  27. Reference directions in two dimensions
  28. It is easy to describe something when you are looking at one dimension, but sometimes giving out directions isn’t that easy.
  29. Sometimes it may take two directions before reaching your destination, which can be referred to as two dimension.
  30. Locating a position in two dimensions
  31. Very similar to describing location in one dimension, but instead of just giving out one direction, you are giving two directions or, in other words, making a left or right turn.
  32. Describing changes in positions
  33. Motion relative to a reference point
  34. When it comes to reference point, it helps in determining whether or not something is in motion.
  35. Motion
  36. The process of changing position
  37. Based on what you choose as your reference point
  38. Distance and displacement
  39. It’s easy to get from Point A to Point B when there is nothing in the way, because you are going in a straight line, but sometimes, it isn’t always the case.
  40. In some cases, the distance or length may take longer due to barriers, so here is the question, how do you get past those barriers?
  41. The easiest way is to go around them, but it takes you off your course and, therefore, causes some displacement.
  42. Displacement
  43. The difference between the initial (first) position and the final position of an object
  44. In other words, displacement is the difference between how it takes you and the distance that it takes to get from your starting point to your final destination.
  45. Example:
  46. The mazes we worked on
  47. Taking a detour due to road construction

Chapter One

Lesson Two

  1. What is speed?
  2. Have you ever wondered how fast you go when either you’re walking or running?
  3. Some of you may say that you move fairly quickly, while others may say that you go very slowly.
  4. What this all boils down to is the speed at which you are going.
  5. Speed
  6. A measure of the distance an object travels per unit of time
  7. Units of Speed
  8. It’s easy to calculate speed by dividing the distance traveled by the time it takes to go that distance.
  9. The SI Unit for speed is meters per second (m/s).
  10. Constant Speed
  11. What happens to your speed when you ride in a car?
  12. Sometimes, you may increase your speed when you are pulling away from your stop sign, or you may even slow your speed down when you are coming to a stop.
  13. However, for the most part, you are maintaining a constant speed.
  14. Constant speed
  15. The rate of change of position in which the same distance is traveled each second
  16. Changing speed
  17. While it’s easy to maintain a constant speed, there are times that your speed can change, and you may want to know what your speed is at that moment.
  18. Typically called instantaneous speed
  19. Instantaneous speed
  20. Speed at a specific instant in time
  21. Average speed
  22. Describing an object’s constant speed is easy if the speed is constant.
  23. But how can you describe the speed of an object when it is speeding up or slowing down?
  24. Easiest way is by calculating the object’s average speed.
  25. Average speed
  26. The total distance traveled divided by the total time taken to travel that distance
  27. Equation for calculating average speed:
  28. Total distance (m)
  29. Total time (s)
  30. Symbol representation:
  31. v̅
  32. Distance-Time Graph
  33. Can help to show how one measurement compares to another
  34. When you study motion, two measurements frequently compared to each other are distance and time.
  35. These graphs are called distance-time graphs
  36. When it comes to constant speed, it is represented as a straight line on a distance-time graph.
  37. Comparing speeds on a distance-time graph
  38. Distance-time graphs can be used to compare the motion of two different objects.
  39. Can also show the slope when comparing two objects
  40. The steeper the line means the greater the slope
  41. Using a distance-time graph to calculate speed
  42. You can use distance-time graphs to calculate the average speed of an object.
  43. Distance-time graphs and changing speed
  44. Remember, that straight lines only represent a constant speed.
  45. Whenever there is a curved line, it typically represents a change in speed.
  46. Velocity
  47. Often, describing the just the speed of a moving object does not completely describe its motion.
  48. Typically, when describing motion, not only do you talk about the object’s speed, but you also talk about the direction that the object may be moving as well.
  49. This is called velocity
  50. Velocity
  51. The speed and direction of a moving object
  52. Representing velocity
  53. One way that you can represent velocity is through the use of an arrow.
  54. The longer the arrow shows a greater speed.
  55. Changes in velocity
  56. Just how a longer arrow can show greater speed, it can also show one other thing and that is a change in velocity.
  57. Velocity changes when the speed of an object changes, when the direction that the object moves changes, or when both the speed and direction change.

Chapter One

Lesson Three

  1. Acceleration
  2. What is acceleration?
  3. A measure of the change in velocity during a period of time
  4. An object accelerates whenever its velocity changes as a result of increasing speed, decreasing speed, or changing direction.
  5. Examples of acceleration
  6. Riding a roller coaster
  7. Pressing down on a gas pedal when the light turns green
  8. Representing acceleration
  9. Just like velocity, acceleration has a direction and can be represented by an arrow.
  10. Difference between an acceleration arrow and velocity arrow.
  11. It all lies in the color of the arrow.
  12. Blue arrow=acceleration
  13. Red arrow=velocity
  14. The length of an acceleration arrow typically indicates the amount of acceleration.
  15. The direction of the arrow also depends on whether or not the speed increases or decreases.
  16. Changing speed
  17. Example
  18. A car stopping and starting at a traffic light
  19. Increasing speed
  20. Whenever an object starts out slowly, it is considered the initial velocity, so it is usually a shorter arrow.
  21. However, as an object increases in speed, its arrow will become longer and represents the final velocity.
  22. Acceleration arrows always points in the same direction as velocity arrows when velocity increases.
  23. Decreasing speed
  24. Whenever an object goes from a faster speed to a slower speed, it shows that acceleration is decreasing.
  25. The initial velocity arrow will always be longer than the final velocity arrow.
  26. The acceleration arrow will point in the opposite direction of the final velocity.
  27. Changing direction
  28. Recall that velocity changes when the direction changes; the same can be said about acceleration.
  29. Calculating acceleration
  30. Acceleration is a change in velocity divided by the time interval during which velocity changes.
  31. In these cases, velocity always represents speed.
  32. Positive and negative can also be taken into consideration when it comes to calculating acceleration.
  33. Positive acceleration can be thought of as speeding up in the forward direction.
  34. Negative acceleration is slowing down in the forward direction as well as speeding up in the reverse direction.
  35. Acceleration equation:
  36. K
  37. Unit of measurement for acceleration
  38. The SI Unit for acceleration is meters per second per second or meters per second squared (m/s2).
  1. Speed-Time Graphs
  2. Recall that graphs can be used in representing distance and time; they can also be used in representing speed and time.
  3. Object at rest
  4. An object at rest isn’t moving, so its speed is always zero.
  5. Constant speed
  6. When it comes to representing constant speed on a Speed-Time Graph, the speed is the same at every point on the line, which means that it represents a horizontal line.
  7. Speeding up
  8. When it comes to representing an object’s increasing speed, the line will typically slant upward with the initial speed being closer to the x-axis and increasing upward to represent an increase in speed.
  9. Slowing down
  10. Whenever a speed decreases, it is represented by a downward slanted line.
  11. The speed is away from the x-axis because of the high speed, but as the speed decreases, then it will get closer to the x-axis.
  12. Limits of speed-time graphs and distance-time graphs
  13. Just like any type of graph, there are always benefits to them and limits to them.
  14. Distance-time graphs
  15. Benefits
  16. Show the speed of an object
  17. Limit
  18. Do not describe the direction in which an object is moving
  19. Speed-time graph
  20. Benefits
  21. Show the relationship between speed and time
  22. Limit
  23. Does not show what happens when an object’s velocity changes as the result of its direction