Acceleration
A car's pedals don't set its speed – they set how the speed changes. That quantity has its own name, acceleration, its own slightly odd unit, metres per second each second, and its own graph trick: on a speed-time plot, the pedal you are pressing is simply the slope of the line.
Intro: the pedal misconception, stated and dismantled. Press the accelerator on a motorway and you go from fast to faster; the pedal never knew your speed, only your change.
5.1The rate of the rate
Acceleration = how much velocity changes, per second: the same “per second” move as chapter 4, applied one floor up. The unit m/s per second read slowly and without apology (the courses will write m/s²). +3 means gaining, −6 means shedding; the sign grammar carries straight over.
5.2Three pedals on a graph
The figure: accelerate, coast, brake – climb, flat, fall on the v–t graph. The quiet bombshell in “coast”: no pedal means the speed keeps, not fades. Everyday floors hide this behind friction; the figure’s honest car does not. Galileo saw through the fog first, and chapter 1 of the classical course starts exactly there.
5.3Free fall: nature’s stuck accelerator
Drop anything: it gains very nearly 10 m/s of downward speed every second, feather-and-hammer caveats honestly stated (air is a hidden brake; on the Moon they land together). The number g ≈ 10 m/s per second introduced as a measured fact about our planet – the why is deliberately left as chapter 6’s cliff.
5.4Why acceleration is the star
Position and velocity are descriptions; acceleration is where the plot happens, because – next chapter’s reveal – acceleration is the one of the three that something in the world has to cause. The primer’s ladder x → v → a is complete; one question remains: who presses nature’s pedals?