Lecture on Constant Acceleration (Chapter 2)

Overview

• Displacement: Represented by 's', is a vector measuring distance from a starting point to an endpoint.
• Time (t): Independent variable in displacement-time graphs.
• Velocity: Gradient of a displacement-time graph.

Graphs in Constant Acceleration

Displacement-Time Graph

• Horizontal Line: Stationary object (no change in displacement).
• Straight Diagonal Line: Constant velocity, velocity = gradient.
• Curved Line: Increasing velocity, indicates acceleration.
• Velocity as Gradient: Velocity is the rate of change of displacement (ds/dt).
• Average Velocity vs. Average Speed
  • Average velocity = total displacement/time.
  • Average speed = total distance traveled/time.

Velocity-Time Graph

• Gradient: Represents acceleration (dv/dt).
• Horizontal Line (y=0): Stationary object.
• Horizontal Line (y>0): Constant velocity.
• Diagonal Line: Constant acceleration.
• Area under the graph: Represents displacement.
  • If velocity is positive, area = displacement.
  • If velocity is negative, area = distance.

Acceleration-Time Graph

• Horizontal Line at x=0: Zero acceleration, constant velocity.
• Horizontal Line at y>0: Increasing velocity (positive acceleration).
• Horizontal Line at y<0: Decreasing velocity (negative acceleration).
• Area under the graph: Represents velocity.

Integration and Differentiation

• Velocity: Integral of acceleration.
• Displacement: Integral of velocity.
• Differentiation: Provides rate of change (velocity from displacement, acceleration from velocity).

Suvat Equations (Constant Acceleration Formulas)

• Variables:
  • S = Displacement
  • U = Initial velocity
  • V = Final velocity
  • A = Acceleration
  • T = Time
• Common Equations:
  • V = U + AT
  • V² = U² + 2AS
  • S = UT + ½AT²
  • S = VT - ½AT²
  • These equations are derived from velocity-time graphs.

Example Problems

1. Stone Sliding on Ice: Application of suvat to find distance and speed at a certain point.
2. Ball Thrown from Tower: Calculating height and speed using suvat equations.
3. Velocity-Time Graph Analysis: Sketching and analyzing graphs based on initial conditions.
4. Car and Bike Race: Using graphs and equations to find acceleration and time to overtake.
5. Stone Dropped from Cliff: Calculating time and speed of free fall.

Important Notes

• Units: Ensure correct units (meters, seconds, m/s²).
• Graphs: Recognize and analyze key characteristics.
• Problem-solving: Draw diagrams, list known variables, choose the right formula.
• Air Resistance: Consider impact on calculations if applicable (greater force on larger, faster objects).

Conclusion

• Practice: Essential for mastering problem-solving with constant acceleration.
• Feedback: Encouraged to seek help and clarify doubts through comments or further examples.