Position, displacement and distance
You will be able to: Distinguish position, signed displacement and total distance for a trip with a reversal.
Can you travel without ending up displaced?
You start at the 2 m floor mark, walk to 8 m, then return to 5 m. You walked 9 m but ended only 3 m to the right of where you began.
A useful starting point: Add and subtract vectors →
Words and symbols before equations
- Position x
- Location relative to a chosen origin, measured in metres (m).
- Displacement Δx
- Final position minus initial position, in m.
- Distance
- Total length of the path, in m; never negative.
- Point model
- Treat an object as a point when its size and internal motion do not matter.
What this picture assumes
One-dimensional trip: 2 m → 8 m → final position. Legs are straight; the diagram shows the path order, not elapsed time.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Displacement 3 m; distance 9 m. The final position is 5 m.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Choose an origin and positive direction before calculating. Your position changes if the origin moves, but the displacement between two fixed events does not change merely because the coordinate origin is shifted by a constant.
For each leg, compute final minus initial. The outward leg gives +6 m and the return gives −3 m. Displacement adds these signed changes: +3 m. Distance adds their magnitudes: 9 m.
For a smooth one-dimensional path, displacement is ∫v dt and distance is ∫|v| dt. The integral symbol means accumulation over an interval. When velocity changes sign, split the interval at the reversal before adding distances. A zero velocity at one instant does not always imply a reversal; check signs on both sides.
| Quantity | Displacement | Distance |
|---|---|---|
| Meaning | Change from start to finish | Total path length |
| Can cancel on return? | Yes | No |
| Unit | m | m |
A worked example, step by step
A cart moves from x = −2 m to x = 4 m, then to x = 1 m. Find displacement and distance.
- Fix +x to the right and keep that direction for both legs.
- The leg displacements are 4 − (−2) = +6 m and 1 − 4 = −3 m.
- Total displacement is final minus initial: 1 − (−2) = +3 m.
- Distance is |6| + |−3| = 9 m. The cart finishes 3 m right of its start after 9 m of travel.
Final position is not displacement unless the initial position is zero.
Return exactly to your start. Which quantity is zero?
Compare with an explanation
Displacement is zero. Distance remains positive if you travelled.
Predict. Change one thing. Explain.
Keep the start at 2 m and the turning point at 8 m. Move only the final position. Predict where displacement becomes zero and whether distance also vanishes.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Displacement 3 m; distance 9 m. The final position is 5 m.
One-dimensional trip: 2 m → 8 m → final position. Legs are straight; the diagram shows the path order, not elapsed time.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant position, velocity, acceleration or integral relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionAn object goes from 1 m to 7 m to 3 m. Find both leg displacements, the total displacement and the total distance. Explain the difference.
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Compare with the answer and four-point rubric
- 1 point: Legs: +6 m and −4 m.
- 1 point: Total displacement: +2 m.
- 1 point: Distance: 10 m.
- 1 point: Displacement compares endpoints and can cancel; distance accumulates path length.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What does Δ mean?
Final minus initial.
RECALL 2Can distance be negative?
No; it is an accumulated length.
RECALL 3Why use |v| for distance?
It counts travel in either direction positively.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Position, displacement and distance
- Δx = x_f − x_i.
- Distance = sum of absolute leg displacements for straight legs.
- Continuous motion: Δx = ∫v dt; distance = ∫|v| dt.
Remember: Final position is not displacement unless the initial position is zero.
Conditions: One-dimensional trip: 2 m → 8 m → final position. Legs are straight; the diagram shows the path order, not elapsed time.
Refresh Kid · AP Physics C: Mechanics Unit 1 (official Unit 1) · Objectives 1.2.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 1.2, objectives 1.2.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. This is Mechanics Unit 1: Kinematics. Quantitative motion problems stay in one or two dimensions; the optional spatial view clarifies vector notation. Students should study calculus alongside this course. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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