Velocity
Speed answers 'how fast'; velocity answers 'how fast, and which way' – and that small addition is what lets the minus signs from chapter 3 drive. This chapter's real prize, though, is a picture: a moving dot and its position-time graph, side by side, until 'steep line' and 'fast motion' become the same thought.
Intro: the speedometer reads 50; it does not say toward or away from home. When direction matters – and in physics it almost always does – speed graduates into velocity.
4.1Metres, per second
Velocity as a rate: how much the address changes, per second of waiting. 3 m/s unpacked as a sentence (“every second, x grows by 3 metres”), computed as displacement ÷ time – the d = v × t of chapter 2, met from its other side.
4.2The sign comes along for the ride
Velocity inherits position’s convention: +3 m/s walks the street one way, −3 m/s the other, same tyre wear. Speed is just velocity with the sign forgotten – occasionally what you want, usually a loss of information.
4.3The graph that draws itself
The figure: drive the dot, watch the pen. Steady velocity writes a straight line; steeper is faster; downhill is leftward. Change the slider mid-run and the line bends at that instant – the graph is not a picture of the road, it is a diary of the trip. The skill named: flicking between motion-view and graph-view at will.
4.4Slope is velocity
The chapter’s theorem, stated in words: however much the graph climbs in one second, that is the velocity, always. Practice readings off a few drawn lines. This one sentence is the seed that grows into calculus – a fact mentioned as a promise, not a threat, and then let go.