Physics · Unit 1: Kinematics ·  Activity 1-1-1

Motion Vocabulary — Distance, Displacement, Speed

Before you can measure how something moves, you need words that don't lie to you — starting with the difference between how far you went and where you ended up  ·  1 class day

Starringdistance = total path lengthΔx = x_f − x_i
Unit 1: Kinematics

A runner starts at the 0 m mark, jogs out to 60 m, then jogs back to the 20 m mark.

0m20m40m60m
Distance traveled
60 m + 40 m = 100 m
total path length — scalar, always positive
Displacement
20 m − 0 m = 20 m
x_f − x_i — depends only on start and end

🧭 Plot Summary

Every kinematics problem you'll ever solve depends on getting these three words right. Distance is how much ground an object covers — the length of the actual path, no matter how winding. It only adds up; it never subtracts. Displacement is different: it only cares about where you started and where you ended, measured in a straight line as a change in position, Δx = x_f − x_i. Walk to the end of the hall and back, and your displacement is zero even though your legs are tired and your distance traveled is not.

Speed ties distance to time — it's a rate, the amount of path covered per second. Average speed = total distance / total time. Today, speed and distance both stay scalars: no sign, no direction. That changes in Lesson 1-1-3, once you have displacement's minus signs to work with and "speed" becomes "velocity."

The core distinction

DistanceScalar. Total length of the path traveled. Never negative, never decreases.
DisplacementHow far and which way from start to finish. Δx = x_f − x_i. Can be zero even if you moved a lot.
SpeedScalar rate. Average speed = distance / time. Tells you how fast ground was covered, not which way.

What you will do in this lesson

  • Distinguish distance (scalar, path length) from displacement (directed change in position).
  • Practice reading and marking positions on a number line to find displacement, Δx = x_f − x_i.
  • Build a scenario where distance ≠ |displacement| — the round-trip case.
  • Define average speed = total distance / total time and compute it for multi-leg motion.
  • Preview why direction will matter starting in 1-1-3, once we start using signed numbers.

Why it matters

This vocabulary is the foundation for the rest of Unit 1. In three days, you'll use exactly these ideas in Project 1-1-4: Motion Detector Graph Match, where you have to physically walk a target position-time graph — and the sensor won't care about your intentions, only your actual displacement over time. Later, in Problem 1-3-1: Crosswalk Safety Study, you'll use distance and rate reasoning to argue for where a real crosswalk should go. Get sloppy with distance vs. displacement now, and both of those get a lot harder.

✅ Self-Check Before You Roll On

Check off each item as you get there. These are not grades — they are your own signal.