3.1MechanicsCore

The SUVAT Equations

For motion in a straight line with constant acceleration, five simple quantities — displacement, initial velocity, final velocity, acceleration and time — are linked by four equations powerful enough to answer almost any question you’ll ever be asked about that motion, as long as you can identify which three you already know.

40 min Video by Physics Online Module 3.1 Motion

SUVAT Equations of Motion — A Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Name the five SUVAT quantities and the four standard equations linking them
Select the correct SUVAT equation given the known and unknown quantities
Apply the SUVAT equations to solve straight-line motion problems
Recognise the sign convention needed when acceleration acts against the direction of motion

The five quantities and four equations

The SUVAT equations connect $s$ (displacement), $u$ (initial velocity), $v$ (final velocity), $a$ (acceleration, constant) and $t$ (time). Each equation involves only four of the five quantities, so given any three known values, you can always find a fourth using whichever equation excludes the one remaining unknown.

v = u + a t s = u t + \frac{1}{2} a t^{2} v^{2} = u^{2} + 2 a s s = \frac{1}{2} (u + v) t

The four SUVAT equations (valid only for constant acceleration).

Tip — Write out the five letters (s, u, v, a, t) for every problem and tick off which three are given and which is being asked for — the correct equation is simply the one that doesn’t involve the remaining, unused letter.

Applying the equations

These equations only apply while acceleration is genuinely constant — if a problem describes changing acceleration (or several distinct stages of motion), you must treat each constant-acceleration stage separately.

1Known:

u = 0

a = 1.5

m s⁻²,

t = 8.0

s. Unknown:

s

(so use the equation without

v

2Use

s = u t + \frac{1}{2} a t^{2}

s = 0 \times 8.0 + 0.5 \times 1.5 \times 8. 0^{2} = 0 + 0.5 \times 1.5 \times 64

Answer

s = 48

Tip — Whenever an object decelerates, or acceleration acts against the direction of initial motion (like gravity on a ball thrown upward), give that acceleration a negative sign relative to your chosen positive direction — getting this sign wrong is the single most common SUVAT mistake.

Equation recap

v = u + a t

No s.

s = u t + \frac{1}{2} a t^{2}

No v.

v^{2} = u^{2} + 2 a s

No t.

s = \frac{1}{2} (u + v) t

No a.

Common mistakes to avoid

Using a SUVAT equation when acceleration is not actually constant.

SUVAT only applies to uniform (constant) acceleration — split any problem with changing acceleration into separate constant-acceleration stages.

Forgetting to give deceleration (or gravity opposing initial motion) a negative sign.

Choose a positive direction at the start of the problem, then give every vector quantity (u, v, a, s) the correct sign relative to it — a deceleration is a NEGATIVE acceleration, not just "a smaller number".

Picking a SUVAT equation that still contains the unknown quantity you’re trying to avoid needing.

Always identify the three KNOWN quantities and the ONE you want; choose the equation that excludes the fifth, unused quantity entirely.

Key takeaways

The five SUVAT quantities: s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time).
Four equations, each excluding one quantity: v=u+at (no s); s=ut+½at² (no v); v²=u²+2as (no t); s=½(u+v)t (no a).
SUVAT only applies to constant acceleration — split multi-stage motion into separate constant-acceleration parts.
Always apply a consistent sign convention, giving deceleration (or opposing acceleration) a negative sign.

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The SUVAT Equations

40 min Video by Physics Online Module 3.1 Motion