Library / Foundations: Physics / FPH-02
Foundations: Physics
Mean acceleration
Average acceleration from change in velocity and time.
- Ref
- FPH-02
- Rev
- v1
- Field
- Foundations: Physics
- Result
- a [m/s²]
Δv is the change in velocity (final − initial) with direction; a negative result means deceleration.
Acceleration is how quickly velocity changes; divide the change in velocity by the time it took.
Calculator
m/s²
m/s
s
- Acceleration in g0.2549 g
- Time to reach 100 m/s40 s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Mean acceleration (m/s²) current value 2.5 m/s²
ΔtTime takenKey driver
0.33320
ΔvChange in velocity
0.12512.5
- 1 g is about 9.8 m/s²; people feel accelerations above a few g strongly.
- Braking is negative acceleration; the formula gives a negative value if v falls.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s²) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Δt Time taken | 1 to 60 s | 0.3333 | 20 | 19.67 | +10% | −9.09 % |
| Δv Change in velocity | 1 to 100 m/s | 0.125 | 12.5 | 12.38 | +10% | +10 % |
Sweep of Time taken
| Time taken (s) | Mean acceleration (m/s²) |
|---|---|
| 1 | 20 |
| 1.668 | 11.99 |
| 2.783 | 7.186 |
| 4.643 | 4.307 |
| 7.746 | 2.582 |
| 12.92 | 1.548 |
| 21.56 | 0.9277 |
| 35.97 | 0.5561 |
| 60 | 0.3333 |
Sweep one variable
Mean acceleration (m/s²)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
a
Mean acceleration
What the equation gives you. Everything else feeds it.
Δv
Change in velocity
Final velocity minus initial velocity. Directly proportional.
Δt
Time taken
Elapsed time. Inversely proportional.
Worked example with the values above
- Change in velocity: 20 m/s over 8 s.
- Divide: 20 / 8.
- a = 2.5 m/s².
Assumptions and limits
- Acceleration averaged over the interval.
- Same direction convention for both velocities.
Common mistakes
- Forgetting the sign for slowing down.
- Using total speed rather than change in speed.
Statistics and uncertainty
Both velocity readings carry errors; because Δv is a difference, errors matter most when the two velocities are close.
Where it is used
- Vehicle performance figures.
- Launch and braking decelerations.
Maths you need
- Velocity: speed with direction
- Division: rate = change ÷ time