A Level Maths: SUVAT

🧮 A Level Maths SUVAT: What Are the Equations of Motion?

⚙️ Setting the Scene

When you start Mechanics in A Level Maths, one of the first things you’ll meet — and probably wrestle with — are the equations of motion. These are often called the SUVAT equations, and they form the foundation of almost everything you’ll do in the topic.

They’re not random formulas to memorise; they describe how an object moves when there’s constant acceleration. Once you understand what each letter means and how they fit together, the harder questions — the ones that mix Newton’s Laws, friction, or motion on slopes — suddenly start to make sense.

I always tell students: if you can master the logic behind SUVAT, the rest of Mechanics behaves itself.

🔙 Previous topic:

Previously, you explored What Maths Is In Mechanics? — where you saw how core mathematical skills like algebra, geometry, and calculus underpin the study of motion and forces.

🧠 What “Motion” Really Means

In Maths and Physics, motion simply means a change in position over time. But that one idea covers a lot of different situations — from a ball rolling down a slope to a car slowing at traffic lights or a satellite orbiting a planet.

To describe motion properly, we use a few key quantities:

Displacement (s): how far you’ve travelled in a specific direction.
Velocity (v): your speed with direction.
Acceleration (a): how quickly that velocity changes.
Time (t): the duration of motion.
Initial velocity (u): your starting speed.

Put all those together, and you can predict almost any movement — that’s what the equations of motion are for.

🧩 Three Main Types of Motion

There are three situations you’ll come across again and again.

First, there’s uniform motion, where the object moves at a steady velocity. No acceleration, no surprises — the classic example is a car on cruise control along a straight road.

Then there’s uniformly accelerated motion, where acceleration is constant. A stone dropped from a height or a car speeding up steadily both fall into this category. These are the cases where our equations of motion apply directly.

Finally, there’s non-uniform motion, where acceleration changes — that’s trickier, and you’ll meet it later when calculus comes into play.

📘 The Famous Five (SUVAT)

Every Mechanics student learns these, but the trick is knowing when to use each one.
There are five variables — s, u, v, a, and t — and each equation connects four of them.

Here they are in plain text:

v = u + at
This one links velocity, acceleration, and time.
I call it the “quick check” equation — perfect for short, straight-line motion questions.
s = ut + ½at²
This one gives displacement using the initial velocity, time, and acceleration.
It’s ideal when you know how long something moves for but not how fast it ends up.
v² = u² + 2as
This skips time completely. You’ll use it when you’ve got velocities and distances but no mention of seconds anywhere.

There are also two rearranged versions:

s = vt − ½at²
and
s = (u + v)t / 2

They all come from the same basic principles — acceleration as rate of change of velocity, and displacement as area under a velocity–time graph.

💬 Teacher Tip

When I mark exam papers, I can always tell who’s memorised versus who’s understood.
The students who understand start by jotting down what’s known and unknown — they don’t rush to plug numbers in.
Write down the five letters vertically (s, u, v, a, t) and fill in what you know.
That tiny habit can be worth two marks before you even start your calculation.

🚀 A Quick Example

Let’s bring this to life.

Question:
A ball is thrown upwards with an initial velocity of 12 m/s. Find:
(a) the time taken to reach its highest point, and
(b) its maximum height.

Step 1: Identify what’s known.
At the top, velocity v = 0.
Initial velocity u = 12 m/s.
Acceleration a = −9.8 m/s² (negative because it’s acting downwards).

Step 2: Apply v = u + at.
0 = 12 − 9.8t
So t = 1.22 seconds.

That’s the time to the top — it’ll take the same time to fall back down again.

Step 3: Find the displacement using s = ut + ½at².
s = 12(1.22) + ½(−9.8)(1.22)²
s = 7.3 metres (to 2 significant figures).

So the ball rises just over 7 metres before gravity brings it to a stop.

Exam tip:
Always label the direction you’ve taken as positive — it saves confusion later.
If upwards is positive, then acceleration is negative.
It’s one of those things the examiner looks for in your working.

🔎 Common Mistakes

Mixing up distance and displacement.
Distance is total ground covered. Displacement is how far you are from where you started — they’re only equal if you move in one direction.
Forgetting signs.
If you take it up as positive, then gravity (acceleration) is −9.8 m/s².
Switching signs halfway through is one of the easiest ways to lose accuracy marks.
Forgetting that acceleration must be constant.
The SUVAT equations only apply under constant acceleration — not when it changes or reverses.

Not linking velocity to slope on a graph.
The gradient of a displacement–time graph gives velocity, and the area under a velocity–time graph gives displacement.
Examiners love to sneak one of those in.

🧭 Beyond the Basics

Once you’re confident with the basic equations, you’ll start to see them appear in disguise.
Sometimes they’re wrapped inside Newton’s Second Law (F = ma) questions, where you’re expected to find acceleration first.
Other times, they’ll appear in projectile motion — one direction uses horizontal equations, the other vertical, with gravity acting only vertically.

And then there’s motion on a slope, where your acceleration becomes g sin θ and your reaction force becomes R = mg cos θ.
The same formulas still apply; you just need to resolve forces first.

📏 Why the Equations Work

It’s worth pausing to see where these come from — they’re not magic.

Start with a = (v − u) / t.
That’s just the definition of acceleration.
Rearranging gives v = u + at, which we already know.

If you draw a velocity–time graph, the area under the line represents displacement.
That’s why s = ut + ½at² works — it’s literally the sum of a rectangle (ut) and a triangle (½at²).

Understanding that connection means you can often rebuild the formula in an exam if you blank.
That’s a useful safety net.

⚡ Real-World Uses

You might think these equations are just classroom maths, but they’re everywhere once you start noticing them.

Engineers use them to design car braking systems — predicting stopping distances accurately saves lives.
Sports scientists use them to analyse jump height or sprint acceleration.
Astronomers use them when modelling planetary orbits in simplified systems.

Everywhere an object moves with constant acceleration, these equations quietly sit underneath.

🧩 When They Stop Working

The SUVAT equations are powerful but not perfect.

If there’s air resistance, or acceleration keeps changing, you’ll need calculus or numerical methods instead.
If you’re near light speed (not common in A Level exams, thankfully!), relativity takes over.

But for 99% of A Level Mechanics questions — straight lines, uniform acceleration, gravity acting downwards — these equations do the job beautifully.

💬 Teacher Insight

When students ask why Mechanics feels harder than Pure Maths, it’s usually because the problems look like stories.
There’s more language to decode before the algebra starts.

My advice? Read each question twice — once to picture what’s happening, once to extract the data.
Then write your list of s, u, v, a, t and let the equation do the heavy lifting.

🎯 Next Steps

If you’ve followed this far, you’ve got the foundations for every motion question in A Level Mechanics.
The next layer is learning how to combine these equations with forces, friction, and motion on slopes, which is where they start to come alive.

To keep building confidence, join our A Level Maths booster course — it covers SUVAT, Newton’s Laws, projectiles, and everything you need for top-band marks.

Remember: Mechanics isn’t about memorising formulas.
It’s about thinking through motion — once you can do that, you’re well ahead of the curve.

Author Bio – S. Mahandru

S. Mahandru is Head of Maths at Exam.tips. With over 15 years of teaching experience, he simplifies algebra and provides clear examples and strategies to help GCSE students achieve their best.

🧭 Next topic:

Next, explore A Level Maths: Mechanics – An Introduction to Kinematics — where you’ll start analysing how objects move before considering the forces that cause that motion.

A Level Maths: SUVAT