Position & Velocity: Saying Where, Precisely
Physics starts by replacing 'it moved' with numbers — and the graph of those numbers already answers questions your eyes can't.
Two numbers beat a description
Everything in this course begins with the same move: replace words with measurements. For motion the measurements are position — where something is, relative to a chosen zero — and time. Position needs a sign: +3 m and −3 m are different places on either side of your zero. Choosing the zero and the positive direction is yours to do; nature doesn’t care, but your equations will.
Velocity is how fast position changes, and in which direction:
The sign matters as much as the size. A car at −20 m/s is not slower than one at +20 m/s; it is driving the other way. Speed is velocity with the sign stripped off — useful for speedometers, not enough for physics.
Average hides, instantaneous tells
Drive 100 km in two hours and your average velocity is 50 km/h — even if you spent twenty minutes parked and ten doing 130. The instantaneous velocity is what the speedometer shows right now: the average over a vanishingly small Δt. Most physics statements are about the instantaneous kind.
Read the graph like a sentence
Plot position against time and the motion becomes legible at a glance:
- Flat line — parked. Position isn’t changing.
- Straight slope — steady velocity. Steeper = faster.
- Slope downhill — moving in the negative direction.
- Curving — the velocity itself is changing: next lesson’s subject.
The rule underneath: the slope of the position graph is the velocity. That one idea — a graph’s slope meaning something physical — repeats through all of physics, so the lab below is about making it reflexive.
You are sitting still — and moving at 30 km/s around the Sun. Both are true; velocity only ever means velocity relative to something. Physics lets you pick the reference that makes the problem easy, which is why train-and-platform puzzles feel like tricks: they are just two valid zeros disagreeing.
⚗️ Lab — The Motion Grapher
Drive a cart with a velocity dial and watch both graphs write themselves.
- Hold a steady positive velocity: the position graph draws a straight ramp.
- Set velocity to zero mid-run — the position line goes flat exactly there.
- Go negative and watch position head back down. Slope is velocity, everywhere and always.
Work it by hand — 0 / 2
No multiple choice here: compute the value and type it. Suffixes like 2.5k or 20m are understood; answers within ±2% count.