Linear Motion Lecture Notes

Introduction to Kinematics

• Kinematics: Study of motion of objects without considering forces.
  • Focuses on how objects move and the path they take over time.
  • Describes an object's motion using position, velocity, and acceleration.
• Dynamics: Focuses on why objects move (forces, energy, mass, momentum).

Key Concepts in Kinematics

Position and Displacement

• Position: Where an object is at a single point in time.
  • Measured relative to a reference point (e.g. bottom of a flagpole).
  • One-dimensional motion (e.g. car on a straight road) uses variable X.
• Displacement: Change in position of an object.
  • Calculated as final position minus initial position (ΔX = Xf - Xi).

Measuring and Graphing Position

• Use number line for position, SI unit is meters (m).
• Example: Car starts at 5m, moves to 15m, displacement is 10m.
• Graph position over time using time on x-axis and position on y-axis.
  • Data points plotted for each time interval to show motion.

Velocity

• Velocity: Similar to speed, but includes direction.
  • Average velocity is displacement divided by time (Vavg = ΔX/ΔT).
  • SI unit is meters per second (m/s).
• Represented using variable V and time as t.
• Equation: V = (Xf - Xi) / (Tf - Ti).

Measuring and Graphing Velocity

• Calculate average velocity between positions using time intervals.
• Graph velocity over time using time on x-axis and velocity on y-axis.
  • Shows if motion is constant or variable.

Acceleration

• Acceleration: Change in velocity over time.
  • Describes how velocity changes.
  • SI unit is meters per second squared (m/s²).
• Equation: A = (Vf - Vi) / (Tf - Ti).
• Example: Car accelerates from 0 to 27 m/s in 4.5 seconds, acceleration is 6 m/s².

Measuring and Graphing Acceleration

• Like velocity, calculate average acceleration over time intervals.
• Graph acceleration over time using time on x-axis and acceleration on y-axis.
  • Shows if acceleration is constant or changes over time.

Additional Concepts

• Instantaneous Velocity: True velocity at a specific instant.
• Acceleration due to Gravity: Constant acceleration for objects falling towards Earth, approximately 9.8 m/s².

Jerk and Higher Derivatives

• Jerk: Change in acceleration over time.
  • Possible but not covered in this course.

Recap

• Position: Measured in meters, change gives displacement.
• Velocity: Change in position over time, measured in m/s.
• Acceleration: Change in velocity over time, measured in m/s².
• Graphing helps visualize motion in position, velocity, and acceleration.