Kinematics Concepts Overview

Overview

This lecture introduces key kinematics concepts, focusing on foundational formulas for motion in physics, including displacement, velocity, acceleration, and commonly used kinematic equations.

Displacement and Distance

• Displacement (Δx or Δy) is the change in position: final position minus initial position (vector quantity, has direction).
• Distance measures the total path traveled regardless of direction (scalar quantity, always positive).

Velocity and Speed

• Velocity is the rate of change of displacement over time: v = Δx/Δt (vector, has magnitude and direction).
• Speed is the absolute value of velocity (scalar, only magnitude, always positive).
• Velocity can be positive or negative; speed is always positive.

Acceleration

• Acceleration is the rate of change of velocity over time: a = Δv/Δt.
• Can be calculated as (final velocity - initial velocity) divided by time interval.

Average vs. Instantaneous Values

• Average velocity: total displacement divided by total time (Δx/Δt).
• Instantaneous velocity: limit of average velocity as time interval approaches zero.
• Average acceleration: change in velocity divided by change in time (Δv/Δt).
• Instantaneous acceleration: limit of average acceleration as time interval approaches zero.

Core Kinematic Equations

• Displacement (constant velocity): d = vt.
• Displacement (constant acceleration): d = v₀t + (½)at².
• Velocity (constant acceleration): v = v₀ + at.
• Velocity-squared formula: v² = v₀² + 2ad.

Derivation of Velocity-Squared Formula

• v² = v₀² + 2ad is derived by combining the displacement and velocity equations for constant acceleration.

Key Terms & Definitions

• Displacement (Δx, Δy) — change in position, vector quantity
• Distance — total path length, scalar quantity
• Velocity (v) — rate of displacement change, vector
• Speed — magnitude of velocity, scalar
• Acceleration (a) — rate of velocity change, vector
• Average Value — measured over a time interval
• Instantaneous Value — value at a specific instant (Δt→0)

Action Items / Next Steps

• Practice kinematics problems using the provided formulas.
• Review derivations for the main equations.
• Watch supplemental videos or access worksheets on kinematics as recommended.