Eleventh Grade · Science · week 4

Position, Displacement, and Velocity

Distinguish distance from displacement and average speed from average velocity, and interpret slope on a position-time graph.

Kinematics is the description of motion -- not yet worrying about what causes it (that starts with Newton's laws in a few weeks). The starting point is position: where an object is relative to some chosen origin, which can be positive or negative. Displacement is the CHANGE in position (final position minus initial position) -- a vector, since it has a direction built into its sign. Distance is the total length of the path traveled, a scalar that can never decrease. Someone who walks 40 m to the mailbox and back has traveled a distance of 80 m but has a displacement of 0 m, since they ended up right back where they started.

The same split applies to rate of motion: average speed is total distance divided by total time (always positive), while average velocity is displacement divided by time (a vector, which can be zero or negative). On a position-time graph, the slope of the line IS the velocity -- a steep line means fast, a flat line means at rest, and a line sloping downward means moving in the negative direction. This graphical reading skill will resurface all year.

📋 For the teacher
Teach it (10–15 min):
  • Walk it out physically: pace from one side of the room to the other and partway back, then ask "how far did my feet travel?" versus "how far from where I started am I now?" -- distance versus displacement becomes obvious in your body before it is a formula.
  • Sketch a couple of simple position-time graphs together (or find some online) and practice reading slope as speed and direction purely by looking, before computing anything.
  • Use a round-trip errand (driving to the store and back) as the running example for "distance greater than zero, displacement equal to zero" -- it is intuitive once tied to a real trip.
  • When they compute average velocity, always ask "and what does the SIGN of your answer mean?" so direction stays attached to the number, not an afterthought.
Talk about it:
  • What is the difference between distance and displacement, using your own example?
  • Why can average velocity be zero even when an object has clearly been moving the whole time?
  • What does the slope of a position-time graph tell you about motion?

Mastery looks like: They correctly compute distance, displacement, average speed, and average velocity for a multi-part trip and read direction and speed directly off a position-time graph's slope.

Common stumbles: Treating distance and displacement as always equal (true only for one-directional motion); reporting average velocity without a sign or direction.

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