Acceleration Calculator
This acceleration calculator completes the missing values: enter three of the five quantities initial velocity, final velocity, acceleration, time and distance. Example: from rest at 3 m/s² for 8 s gives a final velocity of 24 m/s (86.4 km/h) and 96 m of distance.
Source: Wikipedia – Gleichmäßig beschleunigte Bewegung. Updated: .
How it is calculated
With uniform acceleration the velocity changes by the same amount a every second: v = u + a·t. Initial velocity u, final velocity v, acceleration a, time t and distance s are linked by four equations; if you know three, the others are fixed.
The formulas
The four equations of motion are v = u + a·t, s = (u + v) / 2 · t, v² = u² + 2a·s and s = u·t + a·t² / 2. The calculator picks the suitable ones for the values you give and checks the result against all four. Example, starting off: u = 0, a = 3 m/s² and t = 8 s give v = 24 m/s (86.4 km/h) and s = 96 m. Example, braking: u = 25 m/s (90 km/h) and a = −5 m/s² down to v = 0 give t = 5 s and s = 62.5 m.
Units and signs
The calculation uses m/s, m/s² and s; speeds in km/h are divided by 3.6. A negative a means braking in the direction of motion. For orientation a is also given in g (1 g = 9.80665 m/s²), about 0.31 g at 3 m/s².
- If time and final velocity are missing, a square root appears; the result is the first solution.
- With a = 0 initial and final velocity are equal and the calculation reduces to s = v·t.
- Air resistance and changing acceleration are not included.
Frequently asked questions
How do you calculate acceleration?
With a = (v − u) / t: change in velocity divided by time. From 0 to 27.8 m/s (100 km/h) in 8 s that is about 3.5 m/s².
What does negative acceleration mean?
That velocity decreases in the direction of motion, so the body is braking. A car with a = −5 m/s² loses 5 m/s of speed every second.
How do you convert km/h to m/s?
Divide by 3.6: 90 km/h is 25 m/s. In the other direction multiply by 3.6. The calculator does this when you choose “km/h”.
Sources and legal basis
- Wikipedia – Gleichmäßig beschleunigte Bewegung
- Wikipedia – Equations of motion
- Wikipedia – Normfallbeschleunigung (g = 9,80665 m/s²)
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