Changing acceleration: qualitative reasoning
Reason about curved motion graphs without a constant-a shortcut.
Still speeding up, but gaining less each second.
Need an earlier step? Start with velocity & acceleration graphs →
Think of a cart whose velocity is positive and continues to rise, while its velocity graph gradually flattens. It is still speeding up. Its acceleration is positive but getting smaller.
Words and symbols you will use
- Positive velocity
- Motion in the chosen positive direction.
- Positive acceleration
- Velocity increases algebraically; a velocity–time graph slopes upward.
- Decreasing acceleration
- That slope gets smaller. It does not necessarily become negative.
Read the picture, one step at a time.
- The whole curve is above zero: the cart moves in the positive direction.
- The curve keeps rising: velocity increases, so the cart speeds up.
- It becomes less steep: the rate of velocity increase, acceleration, decreases.
| Compare | What it means | What follows |
|---|---|---|
| Velocity decreases | The v–t graph falls. | Acceleration is negative. |
| Positive acceleration decreases | The v–t graph rises but flattens. | Velocity still increases. |
| Acceleration reaches zero | The v–t tangent becomes horizontal. | Velocity need not be zero. |
The idea to keep: Use the graph qualitatively here. The familiar constant-acceleration equations do not describe an entire interval in which acceleration changes.
Can I use constant-acceleration equations when acceleration changes?
Not across the whole changing-acceleration interval. Use the shapes and relationships of motion graphs to reason qualitatively.
When acceleration changes, the slope of the velocity–time graph changes. If acceleration remains positive but becomes smaller, velocity still increases; it simply increases less rapidly. Whether speed increases also depends on the sign of velocity.
This lesson emphasizes qualitative reasoning rather than solving variable-acceleration formulas. On a v–t graph, compare tangent slopes. Positive slope means positive acceleration. A flatter slope means smaller acceleration magnitude. A line that looks high on the graph is not necessarily steep.
A reliable approach
- Read the sign of velocity from the graph’s height.
- Read the sign and relative magnitude of acceleration from its slope.
- State whether your conclusion describes velocity or speed, and identify any sign changes.
Work through one example.
A positive v–t curve rises throughout an interval but gradually flattens. Describe velocity, acceleration, and speed.
Follow the worked solution
- Velocity remains positive and increases.
- Acceleration is positive but decreasing toward zero.
- Speed increases, but the increase per second gets smaller.
Decreasing acceleration is not the same as negative acceleration. A positive value can decrease while remaining positive.
Explain it without notes: Distinguish decreasing acceleration from negative acceleration.
Try explaining it now.
Acceleration is positive but gets smaller. Must the object be slowing?
Compare with an explanation
No. If velocity is positive, speed still increases, though less rapidly. If velocity is negative, its speed initially decreases.
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: Distinguish decreasing acceleration from negative acceleration.
Make a prediction. Test it.
Select the rising-and-flattening velocity case. Move the time marker and compare the local slope with the acceleration plot. Explain why slowing growth is not slowing motion.
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 positive v–t graph rises steeply at first and then flattens without becoming horizontal.
- Describe velocity.
- Describe acceleration’s sign.
- Describe how acceleration magnitude changes.
- Explain whether a single constant-a equation is appropriate for the whole interval.
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: Velocity increases and remains positive.
- 1 point: Acceleration is positive because the slope is positive.
- 1 point: Its magnitude decreases as the graph flattens.
- 1 point: No; the changing slope means acceleration is not constant.
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 1Can positive acceleration be decreasing?
Yes, for example from +4 to +1 m/s².
RECALL 2What does a flattening rising v–t curve indicate?
Positive acceleration with decreasing magnitude.
RECALL 3Does AP Physics 1 require general calculus solutions here?
No; focus on qualitative graph analysis for nonuniform acceleration.
Come back tomorrow: answer these with the cards closed. Try again a week later, especially the ones you missed.
Keep the key ideas handy.
Changing acceleration: qualitative reasoning
Core idea: Not across the whole changing-acceleration interval. Use the shapes and relationships of motion graphs to reason qualitatively.
- On v–t: tangent slope → acceleration.
- Constant-acceleration equations require constant a, not just a known average a.
Avoid this: Decreasing acceleration is not the same as negative acceleration. A positive value can decrease while remaining positive.
Remember why: Use the graph qualitatively here. The familiar constant-acceleration equations do not describe an entire interval in which acceleration changes.
| Graph | Height tells you | Slope tells you | Signed area gives |
|---|---|---|---|
| x–t | Position | Velocity | No standard Unit 1 motion quantity |
| v–t | Velocity | Acceleration | Displacement |
| a–t | Acceleration | Not needed here | Velocity change |
Use local slopes qualitatively when acceleration changes.
Explain, don’t just substituteDistinguish decreasing acceleration from negative acceleration.
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.
Need 1:1 help from a live tutor?
Bring your question about changing acceleration: qualitative reasoning. Ask a Refresh Kid tutor to work through the idea and your next problem with you.