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 are studying motion for the first time or revising for your final exams, understanding these five equations and knowing when to apply each one will unlock a huge number of marks. This guide breaks down everything you need to know.

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 is critical: SUVAT equations only work when acceleration is constant. If acceleration is changing, 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 + 1/2 at² (no v)
3. s = vt - 1/2 at² (no u)
4. v² = u² + 2as (no t)
5. s = 1/2 (u + v)t (no a)

You do not need to memorise all five for every exam board. Most GCSE and A-Level formula sheets provide at least the first two. However, knowing all five saves you time because you can jump straight to the equation that matches the variables you have been given.

How to Choose the Right Equation

The trick is simple: look at what you know and what you need to find. You will 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 does not 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, which is equation 2: s = ut + 1/2 at².

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.

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 = 1/2 (u + v)t

40 = 1/2 (12 + 4)t

40 = 8t

t = 5 s

The deceleration takes 5 seconds.

Common Mistakes to Avoid

Mixing Up u and v

This is the single most frequent error. Always be clear about which velocity is at the start and which is at the end. Read the question carefully. “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 is slowing down, the acceleration is negative (assuming you have defined the direction of motion as positive). If a car decelerates at 5 m/s², write a = -5 m/s² in your equation. Forgetting the negative sign will give you a displacement or velocity that is too large. Similarly, for objects falling under gravity when 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. If a question gives speed in km/h, convert it to m/s before substituting. To convert km/h to m/s, 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. Do not skip this step. Write it down explicitly so you do not forget to include it in your equation.

Exam Technique Tips

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

Draw a diagram. For projectile or vertical motion questions, sketch the situation and label the direction you are taking as positive. This helps you assign the correct signs to your values 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 has gone wrong. Develop the habit of sanity-checking your answers against real-world expectations.

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

SUVAT at A-Level

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

If you are studying A-Level Physics, building fluency with SUVAT now will pay dividends 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 always watch your signs. With consistent practice, these problems become routine.

If you are looking for a structured way to practise SUVAT and other GCSE and A-Level topics, UpGrades provides AI-generated practice questions that adapt to your ability level, helping you focus your revision where it matters most.