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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

Solve for
m/s²
m/s
1100
s
160
  • 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

VariableTypical rangeLowest resultHighest resultSwing (m/s²)Local stepChange in result
Δt Time taken1 to 60 s0.33332019.67+10%−9.09 %
Δv Change in velocity1 to 100 m/s0.12512.512.38+10%+10 %

Sweep of Time taken

Time taken (s)Mean acceleration (m/s²)
120
1.66811.99
2.7837.186
4.6434.307
7.7462.582
12.921.548
21.560.9277
35.970.5561
600.3333

Sweep one variable

Mean acceleration (m/s²)Hover, touch, or use the arrow keys on the chart
05101520 125102050 Time taken (s), log scale now 2.5

Variables and how each one contributes

a

Mean acceleration

Result · m/s²

What the equation gives you. Everything else feeds it.

Δv

Change in velocity

m/s · typical 1 to 100

Final velocity minus initial velocity. Directly proportional.

Δt

Time taken

s · typical 1 to 60

Elapsed time. Inversely proportional.

Worked example with the values above

  1. Change in velocity: 20 m/s over 8 s.
  2. Divide: 20 / 8.
  3. 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

Related formulas

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