Position, distance & displacement
Separate the route traveled from the change in position.
Where are you, and how far did you walk?
Need an earlier step? Start with adding signed vectors →
Let a classroom door be position 0. Start 2 m left of it, walk to 5 m right of it, then return to 1 m right of it. Three different questions now have three different answers.
Words and symbols you will use
- Position x
- Your coordinate measured from a chosen zero (the origin), in meters.
- Initial / final
- The beginning / end of the interval; written with i / f subscripts.
- Δ (delta)
- “Change in”: final value minus initial value.
Read the picture, one step at a time.
- Start at −2 m and finish at +1 m. The endpoint is 3 m right of the start.
- Count both legs: 7 m out and 4 m back. You walked 11 m.
- Your final position is +1 m, but your displacement is +3 m. They use different reference points.
| Compare | What it means | What follows |
|---|---|---|
| Final position | Where do you finish relative to zero? | +1 m |
| Displacement | How does finish compare with start? | +1 − (−2) = +3 m |
| Distance | How much route did you travel? | 7 + 4 = 11 m |
The idea to keep: Displacement depends on endpoints. Distance depends on the route. This is why walking back toward the start reduces net displacement while increasing distance.
Can distance and displacement be different?
Yes. Distance measures the route traveled. Displacement compares the final and initial positions and ignores detours.
Choose an origin, a positive direction, and a length unit before writing a position. A classroom door can be x = 0; a desk can be x = −2 m. A negative position describes which side of the origin the desk occupies, not how it is moving.
For translational motion, a point model tracks one representative location instead of the object’s shape or internal structure. This is useful when size and rotation do not affect the question. A round trip can have a long path but zero displacement.
A reliable approach
- Mark initial and final coordinates on one axis.
- Compute final minus initial, preserving signs.
- Add the lengths of the actual legs to find distance.
Work through one example.
A student begins at x = −2 m, walks to +5 m, then returns to +1 m. Find displacement and distance.
Follow the worked solution
- Δx = +1 − (−2) = +3 m.
- First leg is 7 m; second leg is 4 m. Distance = 11 m.
- The endpoint is 3 m right of the start although the student walked 11 m.
Position is not displacement. The final coordinate +1 m is not the displacement +3 m in this example.
Explain it without notes: Sketch a route where the final position is positive but displacement is negative.
Try explaining it now.
You add 10 m to every position coordinate. Does the displacement change?
Compare with an explanation
No. The same added constant cancels in final minus initial position. The origin moves; the physical endpoints do not.
Another explanation, if you need oneOptional external lesson · Flipping Physics
Displacement, velocity and acceleration
This lesson is complete without a video. For another teacher’s explanation, open the original resource below. Pause after a diagram and explain the idea in your own words.
Suggested section 3:12–8:06. Video by Flipping Physics / Jonathan Thomas-Palmer. Refresh Kid is not affiliated with or endorsed by Flipping Physics. These links open another website. Some videos use g = 9.81 m/s²; our examples state g = 10 m/s². Follow the value given in each problem.
After watching: Sketch a route where the final position is positive but displacement is negative.
Make a prediction. Test it.
Set start to −2 m, turning point to +5 m and finish to +1 m. Trace the two legs, then compare the direct endpoint arrow with the traveled path.
Motion graphs · same clock, different quantities
Try two questions.
Two original Refresh Kid questions. Choose an answer, explain it to yourself, then check the reasoning. These are not released AP exam questions.
Show your reasoning.
Original mini-FRQ · 4 points · Self-checkA toy travels from x = +3 m to x = −1 m and then to x = +5 m.
- Find displacement.
- Find distance.
- Repeat the displacement calculation after moving the origin so every coordinate is 10 m larger.
- Explain the agreement.
Your response stays on this page and is not submitted or automatically graded. Copy it before leaving.
Compare with the worked solution & scoring guide
- 1 point: Displacement = 5 − 3 = +2 m.
- 1 point: Distance = 4 + 6 = 10 m.
- 1 point: New coordinates start at 13 m and end at 15 m; Δx = +2 m.
- 1 point: A common origin shift cancels when final and initial positions are subtracted.
Accept an equivalent correct method. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Does changing the origin change displacement?
No, when both positions shift by the same constant.
RECALL 2Can a moving object have zero displacement?
Yes, if it returns to its start over the chosen interval.
RECALL 3When is the point model useful?
When size, shape and internal motion are irrelevant to the motion being studied.
Come back tomorrow: answer these with the cards closed. Try again a week later, especially the ones you missed.
Keep the key ideas handy.
Position, distance & displacement
Core idea: Yes. Distance measures the route traveled. Displacement compares the final and initial positions and ignores detours.
- Δx = x_f − x_i
- Distance ≥ |displacement|
Avoid this: Position is not displacement. The final coordinate +1 m is not the displacement +3 m in this example.
Remember why: Displacement depends on endpoints. Distance depends on the route. This is why walking back toward the start reduces net displacement while increasing distance.
Use endpoint subtraction for displacement; use the actual path for distance.
Explain, don’t just substituteSketch a route where the final position is positive but displacement is negative.
Refresh Kid · AP Physics 1 · Unit 1 · 1.2.A · Check units, direction and model assumptions.
Connect to released AP practice.
2026 · Question 1 · Version J
Use Part A(i) for component velocity graphs and Part A(ii) for a kinematics derivation. The remaining parts use fluid concepts from Unit 8; they are not Unit 1-only practice.
This is a Unit 1 synthesis task to revisit after learning projectile motion. Historical papers may use different timing or course coverage. Official questions remain on College Board’s site; our questions below are original practice.
Browse released years and scoring information ↗Framework alignment: College Board CED, Topic 1.2. Current exam corrections. Checked September 16, 2026. These explanations and practice items are independently authored by Refresh Kid. The simulation is a mathematical model, not experimental data.
About the videos and learning approach
Optional videos are linked to the publisher’s website and YouTube channel with credit. No external video player is loaded on this lesson page. The written lessons, simulations and practice here are independently authored by Refresh Kid.
We combine worked examples, visual models, explanation and recall practice. See the Institute of Education Sciences study guide ↗ for the underlying learning recommendations.
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