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A Level Maths: Mechanics – An Introduction to Kinematics
A Level Maths: Mechanics – An Introduction to Kinematics
Have you ever seen a car speed off from a red light and realised—you’re watching acceleration in action?
Or drop your pen, see it fall, and go, hang on, that’s literally s = ut + ½at² playing out right in front of me.
That’s kinematics. It’s not abstract — it’s motion, measured carefully and described in maths.
Actually, when I first taught this topic, half the class thought “kinematics” meant some kind of physics add-on. Nope. It’s just motion written in algebra.
Right then — let’s build it slowly and see why every exam board loves it so much.
🔙 Previous topic:
“Go back to see how SUVAT introduces the core motion ideas.”
🧭 What Kinematics Really Means
📏 Kinematics is about describing how things move without worrying about what’s pushing or pulling them.
Three simple ideas keep turning up:
- Displacement — distance, but with direction attached.
- Velocity — how quickly position changes.
- Acceleration — how quickly velocity changes.
That’s the whole skeleton of motion.
🧠 I always tell my students: before you grab the calculator, picture what’s actually moving. Is it speeding up, slowing down, changing direction? If you can describe it in words, the equations suddenly make sense.
⚙️ The Famous SUVAT Equations
When acceleration stays constant, five equations join up s, u, v, a and t.
⚙️
- v = u + at
- s = ut + ½at²
- s = vt − ½at²
- v² = u² + 2as
- s = ½(u + v)t
You never need all five — just choose one that fits the numbers in the question.
✅ Good habit: list what you know and what you’re finding before you choose the equation. That alone earns calm marks.
❗ People often miss that ½. Every examiner I’ve met spots it instantly.
Actually, I still make myself write the “½” in full instead of using decimals — it slows me just enough to stay accurate.
📘 Example 1 — Straightforward Acceleration
A car starts from rest, accelerates at 3 m/s² for 6 s.
Find final velocity and distance travelled.
Given: u = 0, a = 3, t = 6.
⚙️ v = u + at = 0 + 3×6 = 18 m/s.
📏 s = ut + ½at² = 0 + ½×3×6² = 54 m.
🧠 Eighteen metres per second — that’s about forty miles an hour, so it feels realistic.
Nice, tidy motion. Constant push, constant gain.
Right, but what if acceleration changes? Hold that thought.
⚙️ Velocity–Time Graphs
Here’s where pictures help. A velocity-time graph shows how speed changes over time.
📏
- Gradient = acceleration.
- Area under curve = displacement.
🧠 I’d draw it on the board — straight line up, neat triangle underneath. That triangle’s area is the 54 m we just found.
And if the graph curves instead, the gradient isn’t constant — acceleration’s changing.
You can still read it, but you’ll need to estimate the area or use smaller steps.
❗ Exam note: always shade the bit you’re finding before touching the numbers. It’s an easy way to avoid losing half a triangle.
📘 Example 2 — Throwing Upwards
Say you throw a ball straight up at 10 m/s. Gravity pulls down at 9.81 m/s².
Let’s take upwards as positive.
⚙️ v = u + at → v = 10 − 9.81t.
At top: v = 0 → t ≈ 1.02 s.
📏 s = ut + ½at² = 10(1.02) − ½(9.81)(1.02²) ≈ 5.1 m.
🧠 I like to check whether that height feels right — about shoulder to ceiling distance. It does.
Then it falls back down, taking the same time. Symmetry is a lovely thing.
Actually — quick sanity check — if your maths gives a higher “top point” than seems possible, it’s probably because you forgot that negative acceleration.
✅ Always pick a positive direction and stick with it.
🪜 Curved Graphs and Non-Uniform Motion
Now, when acceleration isn’t constant, SUVAT no longer works neatly.
That’s when graphs step in.
Gradient at a point = instantaneous acceleration.
Total area = displacement.
If the line dips below the axis, velocity’s negative — the object’s moving back.
Add areas above and below the axis (taking care with signs) to find total displacement.
🧠 I once timed my own sprint using a phone app — the velocity graph curved up, flattened, then dropped. It was the same shape we sketched in class. It’s funny seeing theory turn into data from your own legs.
⚙️ When to Use SUVAT or Graphs
Right — rule of thumb:
- Use SUVAT for constant acceleration.
- Use graphs when acceleration varies or data is given visually.
Actually, exam boards often test this judgement.
If they phrase it as “use a suitable model,” they’re checking you noticed acceleration isn’t steady.
✅ Once you can hop between equations and graphs comfortably, Mechanics starts feeling intuitive rather than memorised.
📘 Real-World Connection
This is everywhere.
A car’s “0–60” time, a plane’s take-off run, even a video game’s racing physics — all pure kinematics underneath.
🧠 Engineers rely on the same equations to plan braking distances and safe landing zones. I sometimes joke that SUVAT is the most useful thing you’ll ever forget by Christmas.
Right then — you can see why examiners keep it near the start of every Mechanics paper.
❗ Common Mistakes (and Fixes)
- Forgetting to set direction signs.
- Mixing up distance and displacement.
- Treating “constant speed” as “no acceleration” even when the object’s turning.
- Using g as positive while “up” is also positive — pick one.
- Skipping units. Always end with “m”, “m/s” or “m/s²”.
✅ Write “Up positive” or “Right positive” beside the first equation.
If you forget mid-question, that tiny note saves your work..
Actually, I’ve seen examiners give benefit of the doubt purely because the sign rule was written clearly at the top.
🧠 Exam Board Notes (AQA | Edexcel | OCR)
AQA often gives velocity-time graphs and asks for area or gradient.
Edexcel loves chained questions: find acceleration, then time, then distance.
OCR likes sneaky “returns to starting point” setups — means total displacement = 0.
I once saw a whole class lose a mark for not spotting that line. So — underline those phrases before you start.
🚀 Next Steps
If you’re halfway there but still second-guessing which equation fits, our A Level Maths crash course walks through kinematics one diagram at a time.
🚀 It uses exactly this teacher-talk rhythm — clear diagrams, slow steps, and board-style worked examples from AQA, Edexcel, and OCR papers.
Anyway, give it a go.
Even one or two questions a night builds the pattern — you’ll start seeing motion everywhere once you get used to describing it.
✅ Quick Recap Table
Concept | Formula / Idea | What It Describes |
Velocity | v = u + at | Change in speed over time |
Displacement | s = ut + ½at² | How far something travels |
Final velocity | v² = u² + 2as | Links speed and distance |
Mean velocity | s = ½(u + v)t | Average motion over time |
Gradient on v–t graph | = acceleration | Steeper = faster change |
Area under v–t graph | = displacement | Visual distance travelled |
🧭 Next topic:
“See how the equations of motion tie everything together.”
Author Bio
S. Mahandru • Head of Maths, Exam.tips
S. Mahandru is Head of Maths at Exam.tips. With over 15 years of experience, he simplifies complex calculus topics and provides clear worked examples, strategies, and exam-focused guidance.