Physics · Mechanics · Module 3
Kinematics: Describing Motion
Sixteen readings, nine sets of worked examples and six practice papers on how motion is described — before anything is said about what causes it.
Motion is not a property of a body. It is a relation between a body and a frame someone chose.
What this module is
Kinematics answers one question: how do we describe a motion completely? Not why the motion happens — that is Module 4 — but what has to be said, and in what language, for the description to be exact.
The answer turns out to be a single structure. Position, velocity and acceleration form a chain: differentiate to move one way along it, integrate to move back. Everything in these sixteen parts is that chain under a different condition, in a different coordinate, or for a different number of bodies.
Results are derived, not quoted.
Every formula here is obtained rather than stated, and every one is given with the condition it depends on. A result you can reconstruct carries its conditions with it; a result you have merely stored does not — and that difference shows up in the exam where the condition fails.
Start here
Work through in order the first time. Each part assumes the one before it, and several results are used later without being re-derived.
K1 — Frames, Position and Displacement
Why “at rest” is an incomplete statement, and what a reference frame actually contains.
Coming from Module 1? The mathematics is assumed, not re-taught. Foundations 4, 5, 7, 8 and 9 do the most work here.
The sixteen parts
Orientation and method first, then one dimension, then two, then bodies that are linked or turning.
Setting up
K1 — Frames, Position and Displacement
There is no absolute rest. Origins, axes, clocks, and why distance is never less than displacement.
K2 — Drawing Physics
Every book shows diagrams; almost none teaches how to make one. An arrow is a claim, and a wrong one is quiet.
Motion in one dimension
K3 — Average Speed and Velocity
A journey has two averages. Why 40 is the wrong answer, and what “half the journey” leaves unsaid.
K4 — Instantaneous Velocity and Acceleration
Shrinking the interval until it disappears. The one criterion for speeding up, and four things v = 0 can mean.
K5 — Position–Time Graphs
Height, slope and curvature are three independent readings. Which curves could be a motion at all?
K6 — Velocity–Time and Acceleration–Time Graphs
The slope is a rate, the area is a total — and the area is displacement for a reason that is not dimensional.
K7 — Uniform Motion
Meeting problems, and the discipline of rejecting an answer that is correct but inadmissible.
K8 — Constant Acceleration and Free Fall
Four equations from one assumption, and a quadratic whose coefficients contain the symmetry of a thrown ball.
K9 — Variable Acceleration
When a depends on t, x or v — three cases, three different moves. Advanced
K10 — Piecewise Motion
One journey, changing equations. The clock never resets, and neither does the velocity.
Motion in two dimensions
K11 — Motion in Two Dimensions
One motion described in two coordinates. The angle between v and a can be anything.
K12 — Projectile Motion
Two independent motions sharing one clock. The range formula holds only when the ground is level.
K13 — Relative Motion
One subtraction, three costumes. Rivers, rain and crosswind are the same triangle.
Linked and turning
K14 — Constraint Kinematics
A constraint does not tell a particle how to move. It tells it which motions are allowed. Advanced
K15 — Circular and Angular Kinematics
Acceleration has two jobs. Constant speed is not the same as no acceleration.
K16 — Revision and Formula Sheet
Every equation with the condition it depends on, twenty-one traps in one place, and a reference table.
Worked examples
Forty-eight problems across nine sets. Each is chosen because a remembered rule would get it wrong.
Averages
Four journeys. Why a cyclometer and a stopwatch disagree, and why equal distances always give the smaller answer.
Position–Time Graphs
Read one, build one from a description, and judge which of five curves could be a motion.
Constraints
A movable pulley does not always give a factor of two, and three blocks with two strings do not have one degree of freedom. Advanced
Drawing Physics
Six diagrams, two of them wrong. Find the false claim before reading the diagnosis.
Frames, Journeys and Motion in Stages
Move the origin and every position changes; displacement does not. Five problems on what survives a change of description.
Constraints Without Strings
A ladder, a wedge, a scissor lift, a crank, a rope and a spinning hoop — sharing nothing but a fixed length and a derivative. Advanced
Which Direction to Resolve Along
Six problems where the difficulty is not the differentiation but deciding what to project onto — and once, when not to. Advanced
Limits and Boundaries
How far, how high, how fast at most — and what cannot be reached at all. Advanced
The Deceptively Simple
Averages, steady motion and falling bodies — six problems where a plausible method gives a wrong answer that looks entirely reasonable.
Companion pieces
Not examined, and the sixteen parts stand complete without them. They answer questions the module raises and does not settle.
Beyond Acceleration: Jerk, Snap and the Rest
The chain does not end at the second derivative. Why physics stops there anyway — and why railway curves are not circular arcs.
The Techniques, By Name
Vieta’s formulas, separation of variables, the osculating circle — tools this module uses without ever naming. A method you cannot name is one you cannot look up.
Practice
Six papers, 159 questions. No answers are given — and no question names the part it comes from, because deciding that is most of the work.
NEET Practice: Kinematics
Forty multiple-choice questions in forty-five minutes, at the level and pace of the paper itself.
JEE Main Practice: Kinematics
Forty questions in sixty minutes, spanning the whole module from frames to circular motion.
JEE Main: Kinematics Numerical
Twenty multi-part problems requiring full working. Several are quicker by structure than by algebra.
JEE Advanced: Kinematics Numerical
Fifteen Advanced problems — and one of them has no solution, which is the answer. Advanced
Engineering: Kinematics Numerical
Twenty calculus-based problems at university level, several rewarding the choice of which variable to integrate against.
Frames, Constraints and Coupled Motion
Twenty-four questions on reference frames, strings and pulleys, wedges and motion in stages — the parts most practice sets skip.
If a question defeats you, K16 maps twelve physical questions to the tool each one needs — so you can work out which part applies rather than be told.
What comes after
Every acceleration in these thirty-three posts was given, assumed, or read off a graph — never explained. Module 4 asks where accelerations come from.
The description you now have is what makes that question answerable: Newton’s second law relates force to acceleration, and acceleration is something you can compute, measure and reason about in any coordinate system, for any path, for linked or free bodies.
A moving object became a function. A constraint became an equation. A collision became the equality of two positions at one time. None of those translations was forced on us by the world — we chose them, because they work.
Sixteen parts · nine worked-example sets · two companions · six practice papers · 37 diagrams · free, complete, no sign-up
Every correction made to this module is listed on the corrections page.