Lecture on Kinematics: Space, Time, and Motion

Introduction

• Theme: Space, time, and motion
• Topic: Kinematics
• Definition: Study of objects and their motion without consideration of forces
• Goal: Use known/measured values and mathematical models (equations) to solve for other values of an object's motion

Key Values of Motion

1. Position
   • Definition: Location of an object based on a reference point
   • Reference Point: Agreed-upon point in the universe (e.g., origin of coordinate axes)
   • Example: Using shapes and x-axis to describe positions numerically
2. Displacement and Distance
   • Displacement: Vector quantity measuring change in position in a straight line
   • Distance: Scalar quantity measuring total length traveled
   • Example: Traveling from home to a restaurant, and stopping at an ice cream truck
3. Velocity
   • Definition: Rate of change of position
   • Calculation: Displacement divided by time (unit: meters per second)
   • Difference from Speed: Speed is a scalar quantity using distance; velocity is a vector quantity using displacement
   • Types:
     • Instantaneous Velocity: Speed at a specific moment
     • Average Velocity: Speed over the entire journey
4. Acceleration
   • Definition: Rate of change of velocity
   • Calculation: Change in velocity divided by time (unit: meters per second squared)
   • Types:
     • Increasing Velocity: Getting faster
     • Decreasing Velocity: Getting slower

Kinematic Equations (SUVAT equations)

• Purpose: Predict and solve for unknown values of objects in motion
• Symbols: s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time)
• Conditions: Only for objects under uniform acceleration (constant acceleration)

Uniform vs. Non-Uniform Motion

• Uniform Motion: Constant acceleration
• Non-Uniform Motion: Changing acceleration (e.g., hilly surfaces, air resistance)
• Importance: Knowing whether motion is uniform or non-uniform is crucial for problem-solving

Projectile Motion

• Definition: Objects moving in vertical and horizontal dimensions, forming a parabolic path
• Horizontal Motion: Uniform acceleration of zero in absence of air resistance
• Vertical Motion: Uniform acceleration of -9.81 m/s² due to gravity
• Effect of Air Resistance:
  • Horizontal Motion: Decreases acceleration, reducing range
  • Vertical Motion: Causes greater downward acceleration when moving up, and slows downward acceleration when moving down

Terminal Speed

• Definition: Maximum velocity where an object stops accelerating
• Condition: Occurs when air resistance force equals gravitational force, resulting in constant velocity

Conclusion

• Application: Understanding concepts to solve real-world motion problems