Acceleration, signs & changing speed
Use velocity and acceleration together to decide whether speed changes.
A left-moving cart gets faster.
Need an earlier step? Start with scalars, vectors & direction →
A cart moves left at 2 m/s. One second later it moves left at 4 m/s. Choose right as positive. Its velocity changes from −2 to −4 m/s: more negative, and faster.
Words and symbols you will use
- Velocity v
- How quickly position changes, including direction; measured in m/s.
- Acceleration a
- How quickly velocity changes; measured in m/s².
- m/s²
- Meters per second of velocity change, per second of elapsed time.
Read the picture, one step at a time.
- Both arrows point left, so both velocities are negative.
- The second arrow is longer: speed rose from 2 to 4 m/s.
- Velocity change is −4 − (−2) = −2 m/s. Over 1 s, average acceleration is −2 m/s².
| Compare | What it means | What follows |
|---|---|---|
| v positive, a positive | Same sign | Speed increases. |
| v negative, a negative | Same sign | Speed increases. |
| v positive, a negative | Opposite signs | Speed decreases until a stop. |
| v negative, a positive | Opposite signs | Speed decreases until a stop. |
The idea to keep: Negative acceleration points in the negative direction. It does not automatically mean slowing. At a turning instant v = 0, inspect the motion immediately before and after.
Does negative acceleration always mean slowing down?
No. In one dimension, speed increases when velocity and acceleration have the same sign and decreases when their signs oppose.
Acceleration describes a change in velocity, not the amount of velocity itself. A car can move quickly with zero acceleration, or be momentarily at rest with nonzero acceleration. Always compare the direction of velocity with the direction of acceleration.
With right positive, a car moving left has negative velocity. If its acceleration also points left, its velocity becomes more negative and its speed increases. If acceleration points right, the car slows until it stops; continued rightward acceleration then makes it move right.
A reliable approach
- Write the initial and final signed velocities.
- Compute Δv = v_f − v_i, then divide by elapsed time.
- Use both velocity and acceleration signs to discuss speeding up or slowing down.
Work through one example.
A cart changes from −6 m/s to −2 m/s in 2 s. Find average acceleration and describe its speed change.
Follow the worked solution
- Δv = −2 − (−6) = +4 m/s.
- a_avg = 4/2 = +2 m/s².
- Speed decreases from 6 to 2 m/s even though acceleration is positive.
An acceleration sign refers to a chosen direction. It is not a universal label for speeding up or slowing down.
Explain it without notes: Give a case where negative acceleration increases speed.
Try explaining it now.
A cart has v = −5 m/s and a = +2 m/s². Is it speeding up at that instant?
Compare with an explanation
No. The vectors oppose, so speed is decreasing. If that acceleration continues past the stop, the cart reverses and then speeds up.
Another explanation, if you need oneOptional external lesson · Flipping Physics
Seeing velocity and acceleration directions
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 4:48–7:53. 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: Give a case where negative acceleration increases speed.
Make a prediction. Test it.
Set initial velocity +6 m/s and acceleration −2 m/s². Scrub through 3 s. Watch the velocity arrow reverse while the acceleration remains negative.
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 cart begins with v = +6 m/s and maintains a = −2 m/s² for 5 s.
- Find v at 2 s.
- Find when it stops.
- Find v at 5 s.
- Describe how speed changes before and after the stop.
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: v(2) = 6 − 4 = +2 m/s.
- 1 point: 0 = 6 − 2t gives t = 3 s.
- 1 point: v(5) = −4 m/s.
- 1 point: Speed falls until 3 s, then rises as the cart moves in the negative direction.
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 acceleration be nonzero when velocity is zero?
Yes, such as at the highest point of an upward toss.
RECALL 2What does m/s² describe?
Change in velocity, measured in m/s, per second.
RECALL 3Can constant speed involve acceleration?
Yes, if the direction of velocity changes; motion then is not a straight-line constant velocity.
Come back tomorrow: answer these with the cards closed. Try again a week later, especially the ones you missed.
Keep the key ideas handy.
Acceleration, signs & changing speed
Core idea: No. In one dimension, speed increases when velocity and acceleration have the same sign and decreases when their signs oppose.
- a_avg = (v_f − v_i)/Δt
- In 1D: same nonzero signs → speeding up; opposite signs → slowing down.
Avoid this: An acceleration sign refers to a chosen direction. It is not a universal label for speeding up or slowing down.
Remember why: Negative acceleration points in the negative direction. It does not automatically mean slowing. At a turning instant v = 0, inspect the motion immediately before and after.
Compare signs at the instant in question; track any reversal separately.
Explain, don’t just substituteGive a case where negative acceleration increases speed.
Refresh Kid · AP Physics 1 · Unit 1 · 1.2.B · 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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