SUVAT equations

Any triple from the five uniformly accelerated motion quantities — not only s and vₖ from v₀, a, t.

Theory and problem: accelerated motion / SUVAT. Only s and vₖ from v₀, a, t: accelerated motion. School braking: decelerated motion.

Result

Enter values — the result shows up here.

How it works

Constant a: any triple from {s, v₀, vₖ, a, t} determines the rest.

SUVAT is the constant-acceleration toolkit: vₖ = v₀ + at, s = v₀t + ½at², vₖ² = v₀² + 2as, s = ½(v₀+vₖ)t. Enter exactly three values — we solve for the rest.

Check: v₀ = 0, a = 3.5 m/s², t = 8 s → s = 112 m, vₖ = 28 m/s. Braking: v₀ = 20 m/s, vₖ = 0, a = −5 m/s² → s = 40 m.

This is not an upgrade of accelerated motion. That page means “s and vₖ from v₀, a, t”. Here — any triple, with inconsistency checks.

Contradictory triples raise an error instead of a silent wrong answer.

After solving, the chart shows s(t) or v(t) over the motion interval.

How to use

Fill exactly three of the five fields; leave two blank.
Use label units (distance, speed, a); time in seconds.
Calculate — read the missing quantities.
If the triple is inconsistent, fix the inputs.
Compare with accelerated / decelerated tools for simpler intents.

Formula

v_k = v₀ + a t

s = v₀t + ½a t²

v_k² = v₀² + 2a s

s = ½(v₀+v_k)t

Real-life examples

From rest

v₀ = 0, a = 3.5 m/s², t = 8 → s and vₖ.

Brake to stop

v₀ = 20 m/s, vₖ = 0, a = −5 → s.

Find a

v₀ = 0, vₖ = 28 m/s, t = 8.

Find t

v₀ = 10 m/s, vₖ = 20 m/s, a = 2 m/s².

Find v₀

s = 100 m, a = 2 m/s², t = 10.

No a (average)

s = 80 m, v₀ = vₖ = 10 m/s → t.

vₖ from s, v₀

s = 50 m, v₀ = 0, a = 4 m/s².

Stopping time

v₀ = 15 m/s, vₖ = 0, a = −6.

Long run

v₀ = 5 m/s, a = 1 m/s², t = 20.

Ways to use this calculator

Problems with “any three knowns”.
Catch inconsistent data sets.
Bridge accelerated and decelerated pages.
Find time from v₀, vₖ, a.
Find a from v₀, vₖ, t.
Warm-up for full 1D kinematics.
s(t) / v(t) after solving.
Compare with plain a = Δv/t.
Drill SUVAT consistency.

Frequently asked questions

How many fields?

Exactly three. Two or four fails validation.

Different from accelerated motion?

Accelerated always does v₀, a, t → s, vₖ. SUVAT accepts any triple.

Can a be negative?

Yes — braking / axis direction. Enter the sign on purpose.

Inconsistent triple?

You get an error instead of a silent wrong answer.

Time units?

Seconds. Don’t mix hour-based speedo habits without converting.

Air drag?

No — constant a.

Which equation is used?

The solver picks equations for the missing unknowns, then checks consistency.

v₀ = vₖ with a ≠ 0?

Only with t = 0 (or a special s) — often flagged as inconsistent if t > 0.

Stopping distance link?

School s = v²/(2a) is decelerated motion; reaction time is a separate road-safety tool.

Chart — s or v?

We prefer s(t); if t is awkward we show v(t) over the solved interval.

What next?

Simplify to accelerated/decelerated, or add reaction time in stopping distance.