Nothing in nature tells you which way is "positive." You pick a direction, draw an arrow for it, and every sign in the problem follows from that one choice.
🧭 Plot Summary
You've already been doing this — Lesson 1-1-1 talked about "away" and "back," Lesson 1-1-2 talked about lines that "rise" and "fall." Today you trade those words for a plus or minus sign attached to a number, which is exactly what a physicist means by calling a quantity a vectorin one dimension: a magnitude with a direction baked into its sign.
Once direction has a sign, displacement gets a formal partner: velocity. Average velocity is displacement over time, v_avg = Δx / Δt — a signed rate, unlike the always-positive average speed from Lesson 1-1-1. Speed is what's left when you strip the sign off velocity: speed = |v|.
The core distinction
What you will do in this lesson
- Choose a positive direction on a number line and defend why the choice is arbitrary but must be consistent.
- Rewrite 'toward' and 'away' language from Lessons 1-1-1 and 1-1-2 as plus and minus signs.
- Formalize velocity: v_avg = Δx / Δt, a signed quantity built on displacement, not distance.
- Catch the sign-means-slowing-down misconception before it hardens.
- Add signed displacements across several legs of a trip to get a single net answer.
Why it matters
Project 1-1-4: Motion Detector Graph Match will grade your walk against a signed velocity graph — if you don't know that a downward slope means negative velocity, not "the sensor made a mistake," you'll fight the equipment instead of the physics. And in Problem 1-3-1: Crosswalk Safety Study, you'll need signed displacement to reason about a pedestrian's position relative to an oncoming car.
✅ Self-Check Before You Roll On
Check off each item as you get there. These are not grades — they are your own signal.