Units 1 - 2

Page 1: Introduction to Motion

• Physics as Mathematical Science

  • Physics relies heavily on mathematical concepts.

  • Emphasis on both conceptual understanding and mathematical aspects.

• Vocabulary of Motion

  • Common terms: fast, stopped, slowing down, speeding up, turning.

  • Expansion of vocabulary: distance, displacement, speed, velocity, acceleration.

• Categories of Quantities

  • Scalars: Defined by magnitude alone (e.g., distance).

  • Vectors: Defined by both magnitude and direction (e.g., displacement).

• Distance vs. Displacement

  • Distance: Scalar quantity; total ground covered (e.g., 12 meters).

  • Displacement: Vector quantity; overall change in position (e.g., 0 meters in the example of the physics teacher).

• Examples of Motion

  • Teacher's movement: 4m East, 2m South, 4m West, 2m North results in 12m distance but 0m displacement.

  • Importance of direction in vector quantities.

Page 2: Understanding Acceleration

• Definition of Acceleration

  • Vector quantity; rate of change of velocity.

  • Acceleration occurs when velocity changes, not necessarily when moving fast.

• Constant vs. Non-Constant Acceleration

  • Constant acceleration: velocity changes by the same amount each second.

  • Non-constant acceleration: velocity changes by varying amounts.

• Free Fall Example

  • Free-falling objects accelerate at a constant rate, covering different distances each second.

• Calculating Average Acceleration

  • Formula: (a_{avg} = \frac{\Delta v}{\Delta t}).

  • Units: m/s², indicating change in velocity over time.

• Direction of Acceleration

  • Depends on whether the object is speeding up or slowing down.

  • Positive and negative acceleration have physical meanings related to direction.

Page 3: Speed vs. Velocity

• Speed

  • Scalar quantity; how fast an object is moving.

  • High speed covers large distances quickly; zero speed indicates no movement.

• Velocity

  • Vector quantity; rate of change of position.

  • Must include direction (e.g., 55 mi/hr East).

• Average Speed vs. Average Velocity

  • Average speed: total distance divided by total time.

  • Average velocity: displacement divided by total time.

• Instantaneous Speed

  • Speed at any given moment, as opposed to average speed.

• Examples of Average Speed and Velocity

  • Physics teacher's average speed: 0.50 m/s; average velocity: 0 m/s due to no displacement.

Page 4: Motion Representation

• Ticker Tape Timer

  • Device used to analyze motion by marking positions at regular time intervals.

  • Creates a visual representation of motion through dot diagrams.

• Dot Diagrams

  • Show position changes over time; distance between dots indicates speed.

  • Can illustrate constant velocity or acceleration.

Page 5: Vector Diagrams

• Vector Diagrams

  • Represent direction and magnitude of vector quantities using arrows.

  • Size of the arrow indicates magnitude; direction indicates the vector's direction.

• Applications of Vector Diagrams

  • Can represent various physical quantities like velocity, acceleration, and force.

  • Important for understanding motion in future physics studies.

Units 3 - 4

Page 1: Introduction to Motion Representation

• Multiple Means of Representation

  • Words, diagrams, numbers, equations, and graphs.

• Focus on Position vs. Time Graphs

  • Describes motion through shape and slope.

  • Relationship between graph shape and object motion.

Page 2: Constant vs. Changing Velocity

• Constant Velocity Example

  • Car moving at +10 m/s results in a straight line with a constant positive slope.

• Changing Velocity Example

  • Car accelerating results in a curved line with a changing positive slope.

• Importance of Slope

  • Slope indicates velocity characteristics:

    • Constant velocity = constant slope (straight line).

    • Changing velocity = changing slope (curved line).

    • Positive velocity = positive slope (upwards).

Page 3: Accelerated Motion Representation

• Curved Lines Indicate Acceleration

  • Curved lines show changing slope, indicating acceleration.

• Negative Velocity Examples

  • Object speeding up in the negative direction = negative acceleration.

  • Object slowing down in the negative direction = positive acceleration.

• Slope as a Tool for Analysis

  • Slope reveals velocity characteristics (small, negative, constant, changing).

Page 4: Determining Velocity from Slope

• Constant Velocity Example

  • Car moving at +10 m/s for 5 seconds shows a slope of +10 m/s.

• Principle of Slope

  • Slope of position-time graph equals the object's velocity.

Page 5: Using the Slope Equation

• Slope Calculation Method

  • Pick two points, determine rise and run, calculate slope.

  • Consistent results across different point pairs confirm accuracy.

Page 6: Velocity vs. Time Graphs

• Constant vs. Changing Velocity

  • Constant velocity results in a horizontal line (zero slope).

  • Changing velocity results in a sloped line (positive slope).

• Slope Indicates Acceleration

  • Zero acceleration = zero slope.

  • Positive acceleration = positive slope.

  • Negative acceleration = negative slope.

Page 7: Speeding Up vs. Slowing Down

• Identifying Speed Changes

  • Speeding up = moving away from the x-axis.

  • Slowing down = moving towards the x-axis.

• Graph Interpretation

  • Positive and negative regions indicate direction of motion.

Page 8: Analyzing Changing Velocity

• Changing Velocity Example

  • Car accelerating at +10 m/s² shows a diagonal line on the graph.

• Slope Equals Acceleration

  • Slope of the line equals the acceleration of the object.

Page 9: Two-Stage Motion Analysis

• Constant and Changing Velocity

  • First stage: constant velocity (zero acceleration).

  • Second stage: acceleration (positive slope).

• Slope and Acceleration Relationship

  • Slope of the line equals the acceleration during each stage.

Page 10: Understanding Velocity and Acceleration

• Slope Interpretation

  • Positive and negative slopes indicate direction and acceleration.

• Slope Calculation Importance

  • Essential for understanding motion dynamics.

Page 11: Using the Slope Equation for Acceleration

• Slope Calculation Steps

  • Identify coordinates, calculate rise and run, determine slope.

• Consistent Results Across Points

  • Validates the slope calculation method.

Page 12: Area Under Velocity-Time Graphs

• Displacement Calculation

  • Area under the line represents displacement.

• Area Formulas

  • Rectangle: Area = b × h

  • Triangle: Area = 1/2 × b × h

  • Trapezoid: Area = (h1 + h2) / 2 × b