Everything you need to know about the SUVAT equations for A Level Maths and A Level Physics — what each variable means, how to derive every equation, which one to pick in any question, and full worked examples.
The SUVAT equations describe how an object moves when its acceleration is constant. They are one of the most important topics in A Level Mechanics and A Level Physics, and they appear in almost every paper. Once you understand what each one does and how to choose the right one, these questions become very manageable.
SUVAT is just an acronym made from the five variables that appear in the equations. Each letter stands for a different quantity in the motion of an object moving with constant acceleration:
The SUVAT equations only work when acceleration is constant. This is the most important condition to check before using them. If acceleration is changing (for example, if a resultant force is changing), you cannot use SUVAT — you would need calculus instead.
Also important: displacement (s) is not the same as distance. Displacement is a vector — it has direction. An object that goes 10 m forward and then 10 m back has travelled a distance of 20 m but has a displacement of zero. In SUVAT questions you always need to define which direction is positive and which is negative before you start.
✅ Key condition: SUVAT equations only apply when acceleration is constant. Always check this before using them. Common scenarios where acceleration IS constant: free fall (a = 9.8 m/s² downward), objects on a slope with friction, cars with constant engine force on a flat road.
There are exactly 5 SUVAT equations. Each one contains four of the five variables and leaves one out. The missing variable is the one you do not have information about in a particular question.
This is the simplest SUVAT equation. It says that the final velocity equals the initial velocity plus acceleration multiplied by time. It comes directly from the definition of acceleration.
Use this equation when you know u, a, and t and want to find v — or any combination where s is not involved.
This equation works because when acceleration is constant, the average velocity is exactly halfway between u and v. Displacement equals average velocity multiplied by time.
Use this when you know u, v, and t and want to find s — or when a is not involved or not needed.
This is the equation that links velocity and displacement without needing time. It is extremely useful in questions where no time is mentioned.
Use this when you know u, a, and s and want to find v — or any situation where t is not mentioned or needed. Very commonly used for objects thrown upward or projectiles hitting the ground.
This is one of the most used SUVAT equations. It gives you displacement when you know the starting speed, acceleration, and time — without needing to know the final speed.
Use this when you know u, a, and t and want s — or when v is not mentioned or needed. Very commonly used for objects dropped from rest (u = 0) or thrown downward.
This is the fifth and often forgotten SUVAT equation. It is the mirror of equation 4 — use it when you know the final velocity instead of the initial velocity.
Use this when you know v, a, and t and want s — or when u is not given or needed. Less commonly tested but can appear in questions where only the landing or end state is described.
Understanding where the equations come from is both good exam preparation and makes them much easier to remember. The derivation of SUVAT equations starts with just two basic facts about constant acceleration motion.
All other three SUVAT equations are derived by combining equations 1 and 2 in different ways:
📘 Can you derive SUVAT using calculus? Yes. Since v = ds/dt and a = dv/dt, integrating a = constant gives v = u + at, and integrating again gives s = ut + ½at². This is the calculus-based derivation method that may appear in some A Level Physics courses and is useful for understanding why the equations only work for constant acceleration.
This is the question most students struggle with most. The answer is always the same: list your five variables and mark what you know. The variable you have no information about tells you which equation to use.
| You do NOT know or need… | Variables you have | Use equation | Formula |
|---|---|---|---|
| s (displacement) | suvat | Eq 1 | v = u + at |
| a (acceleration) | suvat | Eq 2 | s = ½(u+v)t |
| t (time) | suvat | Eq 3 | v² = u² + 2as |
| v (final velocity) | suvat | Eq 4 | s = ut + ½at² |
| u (initial velocity) | suvat | Eq 5 | s = vt − ½at² |
⚠️ Common mistake: Students often try to “guess” the equation rather than listing variables first. This leads to picking the wrong equation and wasting time. Always write down s, u, v, a, t and fill them in before touching the equations.
Below is a complete list of all the rearranged forms of the SUVAT equations. Knowing these saves you time in the exam because you do not need to rearrange in the middle of a question.
| Find | Use this form | From equation |
|---|---|---|
| Find v | v = u + at | Eq 1 |
| Find u | u = v − at | Eq 1 rearranged |
| Find a | a = (v − u) / t | Eq 1 rearranged |
| Find t (from eq 1) | t = (v − u) / a | Eq 1 rearranged |
| Find s (avg vel) | s = ½(u + v)t | Eq 2 |
| Find t (from eq 2) | t = 2s / (u + v) | Eq 2 rearranged |
| Find v (no t) | v = √(u² + 2as) | Eq 3 |
| Find u (no t) | u = √(v² − 2as) | Eq 3 rearranged |
| Find a (no t) | a = (v² − u²) / 2s | Eq 3 rearranged |
| Find s (no t) | s = (v² − u²) / 2a | Eq 3 rearranged |
| Find s (no v) | s = ut + ½at² | Eq 4 |
| Find t (from eq 4) | Use quadratic formula: at² + 2ut − 2s = 0 | Eq 4 rearranged |
| Find s (no u) | s = vt − ½at² | Eq 5 |
✅ Rearranging SUVAT for t: When you need to find t from equation 4 (s = ut + ½at²), you get a quadratic in t. Rearrange to ½at² + ut − s = 0 and then use the quadratic formula. You will usually get two values of t — take the positive one. The negative value is mathematically valid but physically means time before the motion started.
A car accelerates from rest at 3 m/s² for 8 seconds. Find its final velocity.
s is not involved → use Equation 1: v = u + at
Substitute: v = 0 + 3 × 8
Calculate: v = 24 m/s
A ball is thrown upward with initial velocity 15 m/s. Taking g = 9.8 m/s² downward, find the displacement after 2 seconds.
v is not involved → use Equation 4: s = ut + ½at²
Substitute: s = 15(2) + ½(−9.8)(2²)
Calculate: s = 30 + ½(−9.8)(4) = 30 − 19.6
The positive result means the ball is above the starting point: s = +10.4 m
A train decelerates from 30 m/s to 10 m/s with deceleration 4 m/s². Find the distance covered.
t is not involved → use Equation 3: v² = u² + 2as
Substitute: 10² = 30² + 2(−4)s
Simplify: 100 = 900 − 8s
Rearrange: 8s = 800, so s = 100 m
A stone is dropped from rest from a cliff. It falls 45 m. Find the time taken. (Use g = 10 m/s²)
v is not needed → use Equation 4: s = ut + ½at²
Substitute: 45 = 0 + ½(10)t²
Simplify: 45 = 5t²
Solve: t² = 9, so t = 3 s
📘 Want more SUVAT practice questions with full solutions? Our A Level Maths and Physics tutors work through SUVAT problems step by step in every session — with past paper questions and examiner feedback.
Book Free SessionProjectile motion questions are one of the most common applications of SUVAT at A Level. A projectile is any object thrown through the air — a ball, a bullet, a stone thrown from a cliff. The key is to split the motion into two completely separate directions.
Always define a positive direction before you start. The most common convention:
A ball is thrown horizontally at 20 m/s from the top of a 80 m cliff. Taking g = 10 m/s², find (a) the time to reach the ground and (b) the horizontal range.
Vertical: u = 0 (no vertical velocity at launch), s = 80 m (down = +), a = 10 m/s²
Use s = ut + ½at²: 80 = 0 + ½(10)t² → t² = 16 → t = 4 s
Horizontal: a = 0, so horizontal velocity = 20 m/s throughout
s = 20 × 4 = 80 m
This is one of the most searched questions about SUVAT — and the answer depends on your exam board.
⚠️ Check your specific board. Even if SUVAT equations are in the formula booklet, knowing them by heart saves you time in the exam — you do not have to flick back and forth. Most high-scoring students have all 5 memorised.
Whether or not your exam board provides them, knowing the SUVAT equations without looking them up is a real advantage. Here are the best methods for memorising them:
Learn the equations by what each one is missing. Eq1 has no s. Eq2 has no a. Eq3 has no t. Eq4 has no v. Eq5 has no u. Once you know the pattern, the equations follow logically.
The most reliable method. Each day, close the book and write all 5 equations from memory. After 5 or 6 days they will stick permanently. Test yourself by also writing every rearranged form.
If you understand where the equations come from, you can always re-derive any of the last three from equations 1 and 2. This is a reliable backup in an exam if memory fails.
Write the equation on one side and the missing variable + a worked example on the other. Go through the deck before every revision session. Spaced repetition cements them fast.
✅ Memory shortcut: Equations 1, 4, and 5 all have ½ in them. Equations 2 and 3 do not. If you remember that pattern alongside what each equation is missing, you have a reliable internal check.
Our examiner-qualified A Level Maths and Physics tutors cover SUVAT equations, kinematics, projectile motion and every other mechanics topic — with real past paper questions and step-by-step feedback.
Book Your Free Consultation →The 5 SUVAT equations are: (1) v = u + at — missing s, (2) s = ½(u+v)t — missing a, (3) v² = u² + 2as — missing t, (4) s = ut + ½at² — missing v, (5) s = vt − ½at² — missing u. Each equation contains exactly 4 of the 5 variables.
Write down all 5 variables (s, u, v, a, t). Fill in the values you know from the question and mark the one you want to find. The variable that has no information at all is the one to eliminate — choose the SUVAT equation that does NOT contain that variable. This method works every single time.
For Edexcel A Level Maths — yes, they are in the formula booklet. For AQA A Level Maths — no, they must be memorised. For A Level Physics across most boards they are provided on the data sheet. Always check your specific board’s formula booklet before the exam.
For AQA A Level Maths — yes, memorisation is required. For Edexcel — they are given, so memorisation is not strictly necessary. However, even for Edexcel, most tutors and teachers recommend learning them off by heart because it saves significant time in the exam. See our A Level Maths tutoring page for more exam technique advice.
Yes — for projectile motion, apply SUVAT separately in the horizontal and vertical directions. Horizontally: acceleration = 0, so horizontal velocity is constant throughout. Vertically: acceleration = 9.8 m/s² downward. Solve the vertical SUVAT to find time of flight, then use that time in the horizontal calculation to find range.
There are several ways to find time using SUVAT: from equation 1: t = (v − u) / a; from equation 2: t = 2s / (u + v); from equation 4: rearrange s = ut + ½at² into a quadratic and solve using the quadratic formula. The best choice depends on which other variables you know.
The SUVAT equation that does not contain t is v² = u² + 2as (equation 3). This is the equation to use whenever time is not given and not needed in the question.
The SUVAT equation that does not contain final velocity v is s = ut + ½at² (equation 4). Use this when the final velocity is not given and not needed.
There are exactly 5 SUVAT equations. Each one contains 4 of the 5 variables (s, u, v, a, t) and excludes one. This means that for any problem where you know 3 variables and want to find a 4th, there is always exactly one SUVAT equation to use.
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