Chapter 1: Representing Motion

Particle Model and Motion Diagrams

This section introduces the particle model and motion diagrams as foundational tools for describing motion in physics. These concepts simplify the analysis of objects in motion by focusing on their position at specific times.

• Particle Model: Represents an object as a single point ("particle"), ignoring its size and internal motions. Useful for analyzing translational motion and when the object's rotation is negligible.

• Motion Diagram: A graphical representation showing an object's position at equally spaced time intervals. Velocity vectors can be drawn from each position to the next.

• Interpretation:

  • Increasing distance between images: Speeding up.

  • Decreasing distance: Slowing down.

  • Equal distance: Constant speed.

Position and Time

Describes how motion is specified using a coordinate system with an origin and axes.

• Position (x or r): Location of the particle at a particular instant.

• Time (t): The instant at which an event occurs. A time interval () is the duration of an event.

• Displacement (): The change in position. It is a vector quantity (has magnitude and direction).

• Distance: The total length of the path traveled; a scalar quantity (only magnitude).

Velocity and Speed

Velocity describes the rate of motion and its direction, while speed is the magnitude of velocity.

• Average velocity (): Displacement divided by time interval.

• Average speed: Total distance divided by time interval.

A Sense of Scale (Mathematical Tools)

Physics uses mathematical tools to quantify and analyze motion.

• Units: SI units are standard in physics (e.g., meters for length, seconds for time).

• Significant Figures (Sig Figs): Indicate the precision of a measurement.

• Scientific Notation: Used to express very large or small numbers.

Vectors and Scalars

Physical quantities are classified as either vectors or scalars.

• Scalar: Described by magnitude only (e.g., mass, temperature, distance).

• Vector: Described by both magnitude and direction (e.g., displacement, velocity, acceleration).

Key Skills

• Sketching Motion Diagrams: Draw corresponding motion diagrams with position dots and velocity vectors.

• Unit Conversion: Convert between units using conversion factors.

• Applying Sig Fig Rules: Correctly round answers based on the least precise input value.

Chapter 2: Motion in One Dimension

Graphs of Motion (Kinematics)

This section builds on the foundation of Chapter 1, introducing position-versus-time and velocity-versus-time graphs, and developing kinematic equations for motion with constant acceleration.

• Position-versus-Time Graph ( vs. ):

  • Slope: The slope of the vs. graph is the velocity ().

  • Area: The area under the vs. graph is the displacement ().

• Uniform Motion (Constant Velocity):

  • Motion at a constant velocity in a straight line.

  • Acceleration is zero: .

  • Equation:

• Acceleration:

  • Rate of change of velocity; a vector quantity.

  • Average acceleration:

  • Acceleration and velocity can point in different directions:

    • Same direction: Speeding up

    • Opposite direction: Slowing down

• Motion with Constant Acceleration: The cornerstone of one-dimensional kinematics problems. Requires applying the correct kinematic equations.

• Free Fall:

  • Specific case of constant-acceleration motion where the object is only influenced by gravity.

  • Acceleration is the acceleration due to gravity (), which has a magnitude of .

  • Acceleration is always downward, even if the object is moving upward.

Key Formulas (Kinematic Equations for Constant Acceleration)

These equations relate displacement, velocity, acceleration, and time for motion with constant acceleration.

Note: For vertical motion, replace with .

Key Skills

• Interpreting Graphs: Translate between a physical description of motion, a motion diagram, and the vs. and vs. graphs.

• Problem-Solving Strategy: Apply a systematic strategy for solving constant-acceleration problems:

  1. Sketch and visualize the motion.

  2. Define a coordinate system and note the initial/final conditions.

  3. List knowns and unknowns (often is constant).

  4. Choose the correct kinematic equation that links the knowns and the desired unknown.

  5. Solve algebraically and plug in numbers.

• Free Fall Analysis: Recognize free-fall problems and consistently use (if up is positive) and correctly identify the velocity at the highest point ().

Example: A ball is thrown upward with an initial velocity of . Using the kinematic equations, you can determine its position and velocity at any time, and the time it takes to reach its highest point.

Additional info: The notes provide a concise summary of introductory kinematics, suitable for first-year college physics students. The kinematic equations are fundamental for analyzing motion in one dimension, including free-fall and projectile motion.