Lecture 4: Kinematics - Constant Acceleration

Overview

• Final lecture on Chapter 2: Motion, focusing on kinematics.
• Emphasizes the concept of acceleration, a vector quantity that can change in magnitude or direction.
• Focus on constant acceleration where acceleration remains a fixed value (e.g., 9.8 m/s²).

Key Topics

Constant Acceleration

• Simplest form of acceleration, occurs with a constant force (tension, buoyant, gravitational, etc.).
• Common examples:
  • Falling rock
  • Car accelerating at a consistent rate

Characteristics:

• Constant acceleration means the force and acceleration do not vary over time or distance.
• Velocity changes linearly with time under constant acceleration.
• Displacement under constant acceleration follows a parabolic path.

Graphical Representation

• Acceleration vs. Time: Flat line indicating unchanging acceleration.
• Velocity vs. Time: Linear line indicating constant rate of change.
• Position vs. Time: Parabolic curve indicating increasing displacement with time.

Equations Involving Constant Acceleration

Velocity Function

• Formula: ( v = v_0 + at )
  • Where ( v_0 ) is initial velocity, ( a ) is acceleration, ( t ) is time.
• Linear equation of velocity as a function of time.

Displacement Function

• Formula for Displacement (D):
  • ( D = v_0 t + \frac{1}{2} a t^2 )
  • Accounts for initial velocity and the area under the velocity-time graph.

Graph Interpretation

• Velocity-Time Graph:
  • Area under the line is displacement.
  • Slope of the line is acceleration.
• Acceleration-Time Graph: Area represents change in velocity.

Examples

• Example Problem:
  • A car has an initial velocity of 10 m/s.
  • Accelerates at 4.8 m/s² for 4 seconds.
  • Calculate final velocity and distance:
    • Final Velocity: ( v = v_0 + at = 10 + (4.8 \times 4) = 29.2 ) m/s
    • Distance Travelled: ( D = v_0 t + \frac{1}{2} a t^2 = 10(4) + \frac{1}{2}(4.8)(4^2) = 78.4 ) meters

Important Concepts

• Uniform vs Constant Acceleration: Often used interchangeably; uniform is spatial invariance, constant is temporal.
• Slope & Area Under Graphs: Essential for understanding changes in motion.

Applications

• Free Fall & Gravity:
  • Earth's gravity as a constant force (( g = 9.8 ) m/s²).
  • Variance by location slightly affects ( g ).

Conclusion

• Constant acceleration is a foundational concept in physics, providing a basis for understanding motion under uniform forces.
• Important to grasp graph interpretation and algebraic solutions for practical applications in physics.

End of Chapter 2