SUVAT Equations Explained: GCSE & A-Level Physics Guide

The SUVAT equations are the backbone of mechanics in both GCSE and A-Level Physics. Whether you’re meeting kinematics for the first time or cramming before your final exams, these five equations are your ticket to a huge chunk of marks. Get comfortable with them now. You’ll thank yourself later.

What Does SUVAT Stand For?

SUVAT is a mnemonic for the five variables used in kinematics (the study of motion):

• s = displacement (how far an object has moved from its starting point, in metres)
• u = initial velocity (the speed at the start, in m/s)
• v = final velocity (the speed at the end, in m/s)
• a = acceleration (the rate of change of velocity, in m/s²)
• t = time (the duration of the motion, in seconds)

These five variables describe the motion of any object moving in a straight line with constant (uniform) acceleration. That last point matters: SUVAT equations only work when acceleration is constant. Changing acceleration? You need calculus-based methods instead.

The Five SUVAT Equations

Here are all five equations. Each one links four of the five variables, leaving one out:

1. v = u + at (no s)
2. s = ut + ½at² (no v)
3. s = vt - ½at² (no u)
4. v² = u² + 2as (no t)
5. s = ½(u + v)t (no a)

You don’t need to memorise all five for every exam board. Most GCSE and A-Level formula sheets provide at least the first two. But knowing all five saves time—you can jump straight to the equation that matches your variables without rearranging.

A practical priority order: learn equations 1, 2, and 4 by heart. Those three cover the vast majority of exam questions. The others can be derived or looked up on the formula sheet.

How to Choose the Right Equation

The trick is simple. Look at what you know and what you need to find. You’ll always be given three of the five SUVAT variables and asked to find a fourth.

1. Write down what you know (three values) and what you want to find.
2. Identify which variable is missing from the problem entirely.
3. Pick the equation that doesn’t contain that missing variable.

For example, if a question gives you u, a, and t, and asks for s, the missing variable is v. You need the equation without v: s = ut + ½at².

Worked Examples

Example 1: Finding Final Velocity

A car accelerates from rest at 3 m/s² for 8 seconds. What is its final velocity?

Known values: u = 0 m/s (from rest), a = 3 m/s², t = 8 s

Find: v

Missing variable: s (not needed, not asked for)

Equation: v = u + at

v = 0 + (3)(8) = 24 m/s

The car reaches a final velocity of 24 m/s.

Example 2: Finding Displacement

A ball is thrown vertically upward with an initial velocity of 20 m/s. Taking g = 9.8 m/s² downward, how high does it go?

Known values: u = 20 m/s, v = 0 m/s (at the highest point the ball stops momentarily), a = -9.8 m/s² (negative because gravity acts downward, opposing the upward motion)

Find: s

Missing variable: t

Equation: v² = u² + 2as

0² = 20² + 2(-9.8)(s)

0 = 400 - 19.6s

19.6s = 400

s = 20.4 m (to 3 significant figures)

The ball reaches a maximum height of 20.4 metres.

The conceptual sticking point here is recognising that v = 0 at the highest point. For a single instant, the ball isn’t going up or down — it’s stationary. Once that clicks, projectile-style problems become much easier.

Example 3: Finding Time

A cyclist decelerates from 12 m/s to 4 m/s over a distance of 40 m. How long does this take?

Known values: u = 12 m/s, v = 4 m/s, s = 40 m

Find: t

Missing variable: a

Equation: s = ½(u + v)t

40 = ½(12 + 4)t

40 = 8t

t = 5 s

The deceleration takes 5 seconds.

Common Mistakes to Avoid

One of the most common mistakes: Students write u = 0 when the question says “comes to rest” (that’s v = 0) or write v = 30 when the question says “travelling at 30 m/s” at the start (that’s u = 30). This single error probably costs more marks than any other in mechanics. Read the question twice. Underline “from rest” or “to rest” and write the correct variable next to it before doing anything else.

Mixing Up u and v

This bears repeating. Always be clear about which velocity is at the start and which is at the end. “A car travelling at 30 m/s brakes to a stop” means u = 30 and v = 0. Not the other way around.

Forgetting Negative Signs for Deceleration

When an object slows down, acceleration is negative (assuming you’ve defined the direction of motion as positive). A car decelerating at 5 m/s²? Write a = -5 m/s² in your equation. Forgetting the negative sign gives you a displacement or velocity that’s too large. Same applies to objects thrown upward: a = -9.8 m/s².

Wrong Units

SUVAT equations require consistent SI units: metres for displacement, metres per second for velocity, metres per second squared for acceleration, and seconds for time. Speed given in km/h? Convert it to m/s before substituting. Divide by 3.6.

Not Stating “From Rest” as u = 0

Questions often say an object “starts from rest” or “is dropped.” Both mean u = 0 m/s. Write it down explicitly. Don’t skip this step.

Exam Technique Tips

Show every step. Write out your known values, state which equation you’re using, substitute, and solve. Examiners award method marks for each step. Even if your final answer is wrong, you can still pick up 2 or 3 marks out of 4 with clear working.

Draw a diagram. For projectile or vertical motion questions, sketch the situation and label which direction you’re taking as positive. This helps you assign correct signs and avoids confusion.

Check your answer makes sense. If you calculate that a car has a final velocity of 500 m/s after braking, something’s gone wrong. Get into the habit of sanity-checking against real-world expectations.

Practice two-stage problems. At A-Level especially, many questions involve two stages of motion (a car accelerates then decelerates, for instance). Use SUVAT separately for each stage. The final velocity of stage one becomes the initial velocity of stage two.

Two-stage problems are a common stumbling block because students forget to reset their variables between stages. Write “Stage 1” and “Stage 2” as headings. Treat them as separate mini-questions.

SUVAT at A-Level

At A-Level, SUVAT extends into two-dimensional projectile motion. You apply the equations independently to horizontal and vertical components. Horizontally, acceleration is zero (ignoring air resistance), so the equations simplify. Vertically, acceleration is g = 9.8 m/s² downward. Time links the two directions together. Mastering one-dimensional SUVAT at GCSE gives you a solid foundation for this more advanced work.

If you’re studying A-Level Physics, building fluency with SUVAT now will pay off across mechanics, circular motion, and even simple harmonic motion in Year 13.

Summary

The SUVAT equations describe straight-line motion with constant acceleration. Learn what each variable represents, practise identifying which equation to use by spotting the missing variable, and watch your signs. With consistent practice, these problems become routine.

How to Use This Guide

Don’t just read this once and hope it sticks. Print off the five equations, then work through at least ten practice questions from past papers. Time yourself. When you get one wrong, come back here and check which step tripped you up—was it signs, was it u versus v, was it unit conversion? Fix that specific weakness before moving on. If you want adaptive practice that targets your gaps, UpGrades generates questions matched to your current level.