Motion Along a Straight Line — 1D kinematics

📚 Reference: Halliday, Resnick, Krane — Physics (4th ed.), Vol 1, Chapter 2.
Independent treatment; no text or figures reproduced. All scenarios are original.

What this chapter is about

Chapter 1 gave us the tools of measurement. Now the first serious application: motion. If physics is about “how things change”, kinematics is the language of that description — without (yet) worrying about the cause (that’s dynamics, Chapter 4).

Here we focus on one-dimensional motion (straight line). Why?
– The math is easy — vectors reduce to scalars (just + or −)
– Most of the intuition needed for 2D and 3D motion is built right here
– The constant-acceleration formulas (kinematic equations) used throughout physics are derived here

Sections

1. 2.1 — Position, displacement, average velocity — defining a reference frame, distinction between displacement and distance, average velocity vs average speed.
2. 2.2 — Instantaneous velocity and speed — from average velocity to the derivative: v(t) = dx/dt. Graphical interpretation as tangent slope, instantaneous speed, and common pitfalls.
3. 2.3 — Acceleration — a = dv/dt = d²x/dt², average vs instantaneous, the four sign cases, curvature on the x-t plot, and the bridge to Newton’s second law.
4. 2.4 — Constant acceleration and the kinematic equations — deriving the 4 kinematic equations by integration, equation-selection table, stopping distance and the v² scaling, cases where they fail.
5. 2.5 — Free fall — a = -g independent of mass, throw/drop/return, round-trip symmetry, air resistance and terminal velocity.
6. 2.6 — Graphical analysis and motion integration — area under v-t = Δx, Riemann sums, numerical integration (Euler), full derivative/integral table.
7. 2.7 — Worked problems — seven complete step-by-step problems, from average velocity to integration with variable acceleration, each linked to the §2.x tool being exercised.
8. 2.8 — Practice problems — 20 problems across three levels (⭐ easy to ⭐⭐⭐ hard), without step-by-step solutions, with final answers for self-check.
9. 2.9 — Further reading — parallel textbooks (Serway, Kleppner, Feynman), MIT OCW and Khan Academy, PhET simulations, historical experiments.
10. 2.10 — Q&A — 20 frequently asked questions with short answers, each linked to the relevant section.

Prerequisites

From Chapter 1, these tools should be in hand:
– Scientific notation (§1.6) — big/small numbers (speed of light, tiny particle accelerations)
– Dimensional analysis (§1.7) — checking every formula before trusting it
– Significant figures (§1.8) — honest reporting of precision
– factor-label (§1.9) — the km/h ↔ m/s conversion is used throughout this chapter

If any of these feel weak, go back to Chapter 1.

Reading suggestion

Start with §2.1 in order — this chapter builds more strictly on order (each concept rides on the previous). §2.4 (constant-acceleration equations) is the heart of the chapter — every practical problem starts there.

Related experiments:
– Free-fall experiment — §2.5 in practice
– Simple pendulum experiment — connects to §2.4 (gravitational acceleration)