2.6 — Graphical analysis and motion integration
The §2.4 kinematic equations were valid only for constant acceleration. For variable acceleration (air drag, springs, variable-power engines), we…
2.7 — Worked problems — the Chapter 2 toolkit in action
Seven problems that exercise every tool from Chapter 2. Each begins with a scenario, then walks through the full solution — emphasizing which §2.x…
2.8 — Practice problems — 20 exercises for mastery
Twenty problems without step-by-step solutions — for working on your own. Original scenarios, difficulty varies:
2.9 — Further reading and references
Chapter 2 built a foundational toolkit. To go deeper or see different perspectives, these are good resources.
2.10 — Q&A — Frequently asked questions for Chapter 2
Common questions students raise while working through Chapter 2. Each answer is short and direct; links point to the relevant section for deeper reading.
Chapter 3 — Vectors — the language of motion in 2D and 3D
Vectors are the language of 2D and 3D motion — vector addition, components, unit vectors, dot product, and cross product with full practice sets.
3.1 — Scalars and vectors
Physics deals with two kinds of quantities — scalars and vectors. The distinction is simple, but its consequences are deep: from notation, to how you…
3.2 — Vector addition — the graphical method
Adding vectors is not like adding numbers — magnitudes AND directions must combine. The graphical method is direct, intuitive, and the best way to…
3.3 — Components and unit vectors
The graphical method (§3.2) is fine but doesn’t scale. Components are the algebraic tool that makes vector work scalable — 100 vectors as easy as 2.…
3.4 — Adding vectors by components
With the components tool from §3.3, vector addition reduces to simple scalar addition per axis. More accurate than graphical and scalable to many vectors.