Reference frames & choosing an observer
Name the observer before describing motion.
A backpack sits beside you on a moving train.
Need an earlier step? Start with position, distance & displacement →
You and a backpack move with a train at +5 m/s relative to the platform. The backpack stays 2 m ahead of you. A platform observer sees both of you move; you see the backpack stay in the same place.
Words and symbols you will use
- Reference frame
- An observer’s coordinate system and clock used to describe motion.
- Ground position x
- Position measured from the platform’s fixed origin.
- Relative position x′
- Position measured from the moving observer’s origin: x − x_observer.
Read the picture, one step at a time.
- At t = 0, your ground position is 0 m and the backpack’s is 2 m.
- At t = 1 s, your ground position is 5 m and the backpack’s is 7 m.
- Subtract your position each time: 2 − 0 = 2 m and 7 − 5 = 2 m. The relative position stays fixed.
| Compare | What it means | What follows |
|---|---|---|
| Platform frame | Backpack: 2 m → 7 m in 1 s | Velocity = +5 m/s. |
| Your train frame | Backpack: 2 m → 2 m in 1 s | Velocity = 0 m/s. |
The idea to keep: “At rest” needs a reference frame. Both descriptions are valid; mixing a position from one frame with a velocity from another creates mistakes.
Can an object be at rest and moving at the same time?
It can be at rest relative to one observer and moving relative to another. Always name the reference frame.
A backpack resting on the floor of a steadily moving train is stationary in the train frame but moving in the ground frame. Neither statement contradicts the other: they use different observers and different coordinate grids.
For this unit, use inertial frames: nonrotating frames moving at constant velocity relative to one another. Changing to a frame that speeds up or turns needs extra care beyond the simple constant-velocity frame model used here.
A reliable approach
- Name the object and the observer.
- Label each quantity with its frame, such as velocity relative to ground.
- Distinguish shifting the origin from switching to a moving observer.
Work through one example.
A train travels east at 12 m/s. A bag remains on its floor. Describe the bag’s motion in train and ground frames.
Follow the worked solution
- Relative to the train, the bag’s velocity is 0 m/s.
- Relative to ground, its velocity is +12 m/s if east is positive.
- Both observers measure zero bag acceleration while the train velocity remains constant.
“At rest” is incomplete without identifying the observer. A constantly moving frame is not the same as an accelerating frame.
Explain it without notes: Explain why changing the observer can change velocity without changing acceleration.
Try explaining it now.
A bag stays on a bus seat while the bus moves steadily at 18 m/s. Is the bag at rest?
Compare with an explanation
Relative to the bus, yes. Relative to the ground, it moves at 18 m/s. Both descriptions can be correct.
Another explanation, if you need oneOptional external lesson · Flipping Physics
Relative motion refresher
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 20:13–23:54. 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: Explain why changing the observer can change velocity without changing acceleration.
Make a prediction. Test it.
Set object ground velocity equal to observer ground velocity. Switch between ground and observer plots. The object’s relative velocity becomes zero.
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 moving walkway travels at +2 m/s. A bag rests on it.
- Give bag velocity relative to walkway.
- Give bag velocity relative to ground.
- Give bag acceleration in both frames during steady motion.
- Explain why the two velocity answers are compatible.
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: 0 m/s relative to the walkway.
- 1 point: +2 m/s relative to ground.
- 1 point: 0 m/s² in both inertial frames.
- 1 point: The observers use coordinate systems that move relative to each other.
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 1What must be stated with a velocity?
The direction convention and reference frame.
RECALL 2Can two inertial observers disagree about velocity?
Yes.
RECALL 3Do these inertial observers disagree about acceleration?
No, when their axes are parallel and relative velocity is constant.
Come back tomorrow: answer these with the cards closed. Try again a week later, especially the ones you missed.
Keep the key ideas handy.
Reference frames & choosing an observer
Core idea: It can be at rest relative to one observer and moving relative to another. Always name the reference frame.
- x′ = x − ut when frame origins coincide at t = 0.
- For constant relative frame velocity u: v′ = v − u.
Avoid this: “At rest” is incomplete without identifying the observer. A constantly moving frame is not the same as an accelerating frame.
Remember why: “At rest” needs a reference frame. Both descriptions are valid; mixing a position from one frame with a velocity from another creates mistakes.
Use parallel axes in nonrotating frames with constant relative velocity.
Explain, don’t just substituteExplain why changing the observer can change velocity without changing acceleration.
Refresh Kid · AP Physics 1 · Unit 1 · 1.4.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 1.4. 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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