Acceleration Study Notes

Lesson Overview

Focus Question

• What are two ways velocity can change?

Nonuniform Motion Diagrams

• Uniform motion is characterized by a straight line movement with unchanging velocity; however, many objects exhibit nonuniform motion, where velocity varies.
  • Examples of Nonuniform Motion:
  • Balls rolling down hills
  • Cars braking to a stop
  • Falling objects
  • Future modules will address nonuniform motion not confined to straight lines, including:
  • Circular motion
  • Motion of thrown objects (e.g., baseballs)

Describing Nonuniform Motion

• Characteristics of Motion:
  • Uniform motion feels smooth; eyes closed, one perceives motion as still unless navigating curves or significant changes in elevation, like on roller coasters.
  • Diagrams:
  • Diagram 1: Indicates a person at rest (e.g., a runner before the race).
  • Diagram 2: Distances between positions are equal - jogger in uniform motion.
  • Diagram 3: Increasing distances - jogger speeds up.
  • Diagram 4: Decreasing distances - jogger slows down.

Motion Diagram Interpretation

• Indicators of Change in Velocity:
  • Spacing of dots in motion diagrams: The distance increase implies speeding up; decrease indicates slowing down.
  • Length of velocity vectors: Longer vectors signify increase in velocity; shorter for decrease.
• Two Major Indicators:
  • Change in spacing between dots
  • Changes in lengths of velocity vectors

Acceleration in Motion Diagrams

• To represent full movement information:
  • Include acceleration vectors which indicate the rate at which velocity changes.
• Acceleration:
  • Defined as the rate of change of velocity over time.
  • To draw an acceleration vector:
  1. Determine the change in velocity, $ext{Av} = v<em>{ ext{final}} - v</em>{ ext{initial}}$.
  2. Divide by the time interval $ext{At}$.
  • If the acceleration is constant, calculate it with the formula:
    $a = \frac{ ext{Av}}{ ext{At}}$.

Direction of Acceleration

• Acceleration can occur in four situations:
  1. Increasing speed in a positive direction.
  2. Increasing speed in a negative direction (backward).
  3. Decreasing speed in a positive direction.
  4. Decreasing speed in a negative direction (backward).
• The direction of acceleration is critical for determining if an object is speeding up or slowing down.
  • Acceleration in the Same Direction as velocity = Speeding Up.
  • Acceleration in the Opposite Direction to velocity = Slowing Down.
• Positive and negative accelerations are determined by the vector direction relative to the chosen frame of reference.

Velocity-Time Graphs

• Slope Interpretation:
  • The slope of a velocity-time graph indicates the acceleration of the object.
  • If the graph is a straight line, the acceleration is constant.
  • Example: A slope of $5.00 ext{ m/s}^2$ indicates an increase in velocity of $5.00 ext{ m/s}$ in one second.

Average and Instantaneous Acceleration

• Average Acceleration:
  • Calculated as the change in velocity over the time interval:
    $a = \frac{ ext{Av}}{ ext{At}}$ where,
  • $ext{Av} = v<em>f - v</em>i$ and
  • $ext{At} = t<em>f - t</em>i$.
  • Units are in $ext{m/s}^2$.
• Instantaneous Acceleration:
  • The change in velocity at a specific moment in time, determined using tangents on velocity-time graphs.
  • Can vary when acceleration is not constant.

Example Problems

• Example 1: Analyze the Velocity and Acceleration of a Sprinter
  • Observation of velocity changes on a graph, calculating the average instantaneous accelerations at specific times.
• Example 2: Describe the Motion of a Ball Rolling Up a Driveway
  • Analyze initial and final velocities, solve for acceleration and examine directions.

Practice Problems

1. Sketch velocity-time graphs based on provided motions.
2. Calculate the average accelerations over specified intervals based on given scenarios.

Critical Thinking and Application

• Consider real-world applications of acceleration concepts in fields such as transportation and sports.
• Discussions on why certain velocities can be deceptive in relationship to motion and acceleration.