Motion diagrams & equal-time dots
Read equal-time dots without assuming unmeasured motion.
Imagine a camera taking one photo each second.
Need an earlier step? Start with average speed vs. average velocity →
Mark one dot for the cart’s position in each photo. At 0, 1, 2 and 3 seconds, the cart is at 0, 1, 4 and 9 meters. Read the dots in time order, not just from left to right.
Words and symbols you will use
- Motion diagram
- Positions recorded at stated times, drawn on a spatial axis.
- Equal-time spacing
- Each pair of neighboring snapshots is separated by the same amount of time.
- Interval velocity
- Displacement between two snapshots divided by their time separation.
Read the picture, one step at a time.
- The clock advances by 1 s between every pair of dots.
- The gaps grow from 1 to 3 to 5 m. The cart covers more ground in each successive second.
- Its average velocities in those intervals are +1, +3 and +5 m/s. The data are consistent with speeding up to the right.
| Compare | What it means | What follows |
|---|---|---|
| Equal signed gaps | Same displacement each interval | Equal interval-average velocities. |
| Growing gap magnitudes | More distance each equal interval | Larger interval-average speeds. |
| Unknown time gaps | Timing information is missing | Cannot infer speed from spacing alone. |
The idea to keep: Snapshots do not reveal everything between them. These positions fit constant acceleration, but a few dots alone do not prove what happened at every instant.
What does the spacing in a motion diagram tell you?
For dots drawn at equal time intervals, wider spacing means greater average speed between those dots. Read their time order to determine direction.
A motion diagram records positions at successive instants. Equal time gaps are essential: the diagram compares how much distance is covered in the same time. If the time gaps differ, dot spacing alone cannot rank speed.
Number the dots or draw a time-order arrow when an object reverses. At a turning point, successive marks can overlap. Velocity arrows follow the motion; acceleration describes how those velocity arrows change. Do not confuse an arrow of motion with a force arrow.
A reliable approach
- Check that all time intervals match.
- Use successive displacements to compare average velocities.
- Look at how these velocities change to infer acceleration direction.
Work through one example.
At t = 0, 1, 2, 3 s, a cart is at x = 0, 1, 4, 9 m. Describe the pattern.
Follow the worked solution
- Successive displacements are +1, +3 and +5 m in equal 1 s intervals.
- The cart moves right and its speed increases.
- These positions fit x = (1 m/s²)t², a constant-acceleration model with a = +2 m/s² and v₀ = 0.
Increasing dot spacing shows increasing speed only if the time intervals are equal.
Explain it without notes: Explain the difference between a model that fits the dots and a uniquely proven motion.
Try explaining it now.
Two successive gaps are 2 m and 4 m. Does that alone prove the object sped up?
Compare with an explanation
No. You need the elapsed time for each gap. Even equal-time dots describe interval averages; they do not reveal every detail between measurements.
Another explanation, if you need oneOptional external lesson · Flipping Physics
Motion graphs: worked reasoning
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 0:00–6:54. 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 the difference between a model that fits the dots and a uniquely proven motion.
Make a prediction. Test it.
Set v₀ = +6 m/s and a = −2 m/s². Examine the equal-time markers before and after the turn. Use the time labels rather than left-to-right order.
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 tracker records x = 0, 2, 4, 6 m at t = 0, 1, 2, 3 s.
- Find the three interval-average velocities.
- Give the simplest constant-velocity model that fits.
- Can these measurements prove the instantaneous velocity was constant between every pair of samples? Explain.
- Propose an improved measurement to detect brief stops or speed changes.
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: Each interval has average velocity +2 m/s.
- 1 point: x = (2 m/s)t fits all four recorded positions.
- 1 point: No. Unobserved speeding up and slowing down can still give the same interval displacements.
- 1 point: Collect more frequent position measurements with calibrated distance and time scales; finite sampling and measurement uncertainty still limit the conclusion.
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 do equally spaced dots at equal times establish?
Equal average velocities over the marked intervals if direction stays the same. Finer motion between the dots is not resolved.
RECALL 2How can you show a reversal?
Label times so the sequence is clear even if positions overlap.
RECALL 3What indicates slowing in a straight-line diagram?
Successive gaps shrink for equal time intervals before a stop.
Come back tomorrow: answer these with the cards closed. Try again a week later, especially the ones you missed.
Keep the key ideas handy.
Motion diagrams & equal-time dots
Core idea: For dots drawn at equal time intervals, wider spacing means greater average speed between those dots. Read their time order to determine direction.
- Between adjacent dots: v_avg = Δx/Δt.
- Constant velocity → equal signed displacements in equal times.
Avoid this: Increasing dot spacing shows increasing speed only if the time intervals are equal.
Remember why: Snapshots do not reveal everything between them. These positions fit constant acceleration, but a few dots alone do not prove what happened at every instant.
Compare dot spacing only after checking the time labels.
Explain, don’t just substituteExplain the difference between a model that fits the dots and a uniquely proven motion.
Refresh Kid · AP Physics 1 · Unit 1 · 1.3.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 1.3. 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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