Kinematics

Relative motion is not a separate formula set. It is a change in what we call the zero of position, and everything follows from differentiating that change.

Projectile motion is two independent motions sharing one clock. The components don’t know about each other. Time does — and it’s what you carry between the two equations.

At the apex of a projectile the speed is 3 m/s. The acceleration is 10 m/s² downward. They have nothing to do with each other.

The equation changes at each stage boundary. The particle does not — it passes through with the same position and velocity, and the next stage begins where the last one ended.

Acceleration is not a number but a function, and the variable it depends on decides which mathematics will work. Three cases, and the familiar four equations turn out to be the simplest of them.

Four equations that every student memorises, and one assumption that produces all of them — plus a ball passing the same height twice, whose launch speed can be read off the coefficients.

The algebra is faultless and the answer is negative five seconds. A correct equation can produce an answer that must be thrown away, and knowing when is part of the solution.

Do not memorise which feature of which graph gives which quantity. Ask what derivative or integral connects the two axes, and the rule becomes inevitable.

Module 3: Kinematics  ·  Theory  ·  Prerequisites: K4, Foundation 7 Everything K4 obtained by differentiating is visible on a graph without calculating anything. Mahavakya A graph is not a picture of the motion. It is the motion written in a second language, and some things are easier to say there. On this page Height and … Read more

An average describes an interval. To describe an instant, the interval has to disappear — and what survives is a description we construct rather than a number the object carries.