Overview
This lecture covers key concepts and formulas in kinematics, focusing on motion, displacement, velocity, acceleration, and the main kinematic equations used in physics.
Kinematics Basics
- Kinematics studies motion in one or two dimensions (x and y axes).
- Displacement (Δx or Δy) is the change in position: final position minus initial position.
- Displacement is a vector (has magnitude and direction); distance is a scalar (only magnitude).
- Velocity is the rate of change of displacement over time: v = Δx/Δt (vector).
- Speed is the magnitude of velocity and is always positive (scalar).
Acceleration
- Acceleration is the change in velocity over time: a = Δv/Δt.
- Both velocity and acceleration can be positive or negative due to their directional nature.
Average vs. Instantaneous Values
- Average velocity: total displacement divided by total time, v̄ = (x_final - x_initial)/Δt.
- Instantaneous velocity: the velocity at a specific moment; calculated using limits as Δt approaches zero.
- Average acceleration: ā = (v_final - v_initial)/Δt.
- Instantaneous acceleration: limit as Δt approaches zero for Δv/Δt.
- Smaller time intervals provide better approximations for instantaneous values.
Common Kinematic Formulas
- Displacement with constant velocity: d = v × t.
- Displacement with constant acceleration: d = v_initial × t + ½ a t².
- Average velocity under constant acceleration: v_avg = (v_initial + v_final)/2.
- Final velocity: v_final = v_initial + a t.
- Final velocity squared: v_final² = v_initial² + 2 a d.
Derivation Example
- The formula v_final² = v_initial² + 2 a d can be derived by combining and rearranging other kinematic equations.
Key Terms & Definitions
- Displacement — Change in position (vector: has direction).
- Distance — Total path length traveled (scalar: only magnitude).
- Velocity — Rate of change of displacement (vector).
- Speed — Rate of change of distance (scalar).
- Acceleration — Rate of change of velocity (vector).
- Average — Total change over an interval divided by the duration.
- Instantaneous — Value at a specific instant in time.
Action Items / Next Steps
- Practice kinematics problems using provided resources or online videos.
- Review and memorize the common kinematic formulas.
- If assigned, print and complete worksheets on displacement, velocity, and acceleration.