SUVAT and the equations of motion

Physik GCSE Updated Wed 7 Oct 2026

SUVAT is the name for five quantities that describe something speeding up or slowing down at a steady rate. At GCSE you mostly need one equation from the equation sheet and one you recall, but you need to use them with the right signs and units.

Part 1 of 3: Learn it

In short

Only use the SUVAT equations when the acceleration is constant.
Write down the letters you know and the one you want before you choose an equation.
Slowing down means a negative acceleration if you take the direction of motion as positive.

Where this is in your specification

Spec points: AQA 4.5.6.1.5, Edexcel Topic 2, OCR P2.1

Board	Topic: Forces and motion
AQA 8463	4.5.6 (8463); 6.5.4 (8464)
Edexcel 1PH0	Topic 2
OCR J249	P2.1 and P2.2

The five letters

Velocity and displacement have a direction, so they can be negative. Pick one direction as positive at the start of every question and stick to it.

Letter	Quantity	Unit
s	displacement (distance in a given direction)	m
u	initial velocity	m/s
v	final velocity	m/s
a	acceleration	m/s²
t	time	s

The equations you use at GCSE

Acceleration is the change in velocity divided by the time taken. You need to recall this one:

a = (v − u) ÷ t

v² − u² = 2 a s

The second one links speeds and distance with no time in it, and AQA, Edexcel and OCR all print it on the equation sheet. Use it when the question gives you no time and does not ask for one: braking distances, objects dropped from a height, a car speeding up along a slip road.

A-level adds three more equations (v = u + at, s = ut + ½at² and s = ½(u + v)t). The first is just a = (v − u) ÷ t rearranged, so you already know it.

Falling objects

Near the Earth's surface, an object falling with no air resistance accelerates at g = 9.8 m/s² (some papers round it to 10 m/s²; use the value the question gives). If it is dropped, u = 0. Taking down as positive makes a = +9.8.

Quick check

A cyclist speeds up from 4 m/s to 10 m/s in 3 s. What is the acceleration?

Show the answer

a = (10 − 4) ÷ 3 = 2 m/s².

Part 2 of 3: See it worked

Worked examples

Example 1

A car travelling at 25 m/s brakes steadily and stops in 50 m. Find its acceleration.

Known: u = 25 m/s, v = 0, s = 50 m. Want: a. No time, so use v² − u² = 2as.
0² − 25² = 2 × a × 50
−625 = 100a
a = −6.25 m/s²

Answer: The acceleration is −6.25 m/s². The minus sign means it is slowing down: a deceleration of 6.25 m/s².

Example 2

A stone is dropped from a bridge 20 m above the water. How fast is it going when it hits the water? Ignore air resistance and use g = 9.8 m/s².

Take down as positive. Known: u = 0, a = 9.8 m/s², s = 20 m. Want: v.
v² = u² + 2as = 0 + 2 × 9.8 × 20 = 392
v = √392 = 19.8 m/s

Answer: About 19.8 m/s (20 m/s to 2 significant figures).

Common mistakes

Giving v² as the answer. Square-root at the end.
Using +a for something that is slowing down, which gives a negative v² and no answer.
Leaving speeds in km/h. Divide by 3.6 to get m/s: 72 km/h = 20 m/s.
Using SUVAT when the acceleration changes, for example a parachutist before terminal velocity.
Squaring the difference (v − u)² instead of finding the difference of the squares, v² − u².

Quick check

A train slows from 30 m/s to rest at 0.5 m/s². How far does it travel while braking?

Show the answer

0 − 30² = 2 × (−0.5) × s, so s = 900 m.

Part 3 of 3: Test yourself

Check yourself

Answer each one in your head or on paper first, then open it to check.

A cyclist speeds up from 4 m/s to 10 m/s in 3 s. What is the acceleration?

a = (10 − 4) ÷ 3 = 2 m/s².

A train slows from 30 m/s to rest at 0.5 m/s². How far does it travel while braking?

0 − 30² = 2 × (−0.5) × s, so s = 900 m.

Which equation would you use if a question gives u, a and s and asks for v?

v² − u² = 2as, because it has no t in it.

Jobs that use this

Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).

Diese Lernzettel sind auf Englisch, weil sie britischen Prüfungslehrplänen folgen.

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