SUVAT equations: v = u + at, s = ut + ½at²

The SUVAT equations are v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t; s = vt − ½at².

\(\displaystyle v=u+at\) \(\displaystyle s=ut+\tfrac12at^2\) \(\displaystyle v^2=u^2+2as\) \(\displaystyle s=\tfrac12(u+v)t\) \(\displaystyle s=vt-\tfrac12at^2\)

What each letter means

\(s\) displacement
\(u\) initial velocity
\(v\) final velocity
\(a\) acceleration (constant)
\(t\) time

When to use it

For motion in a straight line with constant acceleration, including objects falling freely under gravity.

Worked example

A car moving at \(4\text{ m s}^{-1}\) accelerates uniformly at \(1.5\text{ m s}^{-2}\) for 6 s. Find its final speed and the distance travelled.

\(v=4+1.5\times6\)
\(s=4\times6+\tfrac12\times1.5\times6^2=24+27\)

Answer: \(v=13\text{ m s}^{-1}\), \(s=51\) m

Common mistake

Using them when the acceleration is not constant. Then you need calculus: v = ds/dt, a = dv/dt.

On your course

Course	In the exam
Edexcel A Level (9MA0)	In the Edexcel formulae booklet
Edexcel International A Level	Not in the booklet: learn it
AQA or OCR A Level	Check your board’s formula booklet: AQA formulae booklet (PDF) · OCR A Level Maths assessment page

From our own A Level Maths formula sheets, in our words. Official: Pearson's formulae booklet (PDF) · Pearson's IAL formulae booklet (PDF).

Practise and revise

Practise A Level Maths practice
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Revise IAL M1 kinematics
Print Edexcel A Level (9MA0) one-page formula sheet

SUVAT equations formula card: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t; s = vt − ½at². A Level Math Revision — SUVAT equations formula card. Download the card (PNG) to save or print it.

Questions

What is the SUVAT equations formula?

The SUVAT equations are v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t; s = vt − ½at². s: displacement; u: initial velocity; v: final velocity; a: acceleration (constant); t: time.

Is the SUVAT equations given in the exam?

Edexcel A Level (9MA0): in the Edexcel formulae booklet. Edexcel International A Level: not in the booklet: learn it. AQA or OCR A Level: check your board’s formula booklet. This comes from our own A Level Maths formula sheets; your teacher has the official booklet.

Which suvat equation should I use?

Write down the three quantities you know and the one you want. Use the equation that contains exactly those four letters.

Our own wording, examples and card, checked by A Level Math Revision. Not produced or endorsed by Pearson Edexcel, AQA or OCR.