The big idea: Acceleration tells you how quickly the velocity is changing.
Speeding up, slowing down, and changing direction can all involve acceleration.
Unit: m s⁻² (metres per second, every second).
A car accelerates when it speeds up or slows down. For example, if its velocity increases by 5 m s⁻¹ every second, its acceleration is 5 m s⁻².
Animated graph
Watch the graph build step by step in study mode.
The precise rule: These examples show a car moving forwards.
• Acceleration in the same direction as the velocity → the object speeds up.
• Acceleration in the opposite direction to the velocity → the object slows down.
Acceleration describes how the velocity changes.
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it with your first topic free to keep:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Slope = acceleration: On a velocity–time (v–t) graph, the slope of the line is the acceleration.
Slope = how much the velocity changes ÷ the time it takes.
So a steep line means a big acceleration; a gentle line means a small one.
Animated graph
Watch the graph build step by step in study mode.
The slope: a = Δv ÷ Δt (Δv = change in velocity, Δt = time taken). Cover the one you want — two side by side → multiply; one above the other → divide.
Interactive diagram
Explore the labelled diagram, charts and maps for this topic in full study mode.
A quick note on v = u + at: Acceleration also appears in the equation of motion v = u + at (final velocity = initial velocity + acceleration × time) — one of the suvat equations you'll meet in full in A.1.4. Here we just read the acceleration off the slope of the graph.
A train moving in the positive direction speeds up from 8.0 m s⁻¹ to 20 m s⁻¹ in 6.0 s. Find its acceleration.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Learn what examiners really want
See exactly what to write to score full marks. Our AI shows you model answers and the key phrases examiners look for.
What an a–t graph shows: On an acceleration–time (a–t) graph:
Up the side → the acceleration (m s⁻²).
Along the bottom → the time (s).
So the height of the line tells you the acceleration at that moment — not the velocity. It looks like a velocity–time graph, so always check the axis first.
Animated graph
Watch the graph build step by step in study mode.
What the different lines mean: Flat line above the axis → a steady (constant) acceleration — the velocity keeps increasing.
Flat line on the axis (a = 0) → no acceleration — the velocity stays constant (the object may still be moving).
Flat line below the axis → a steady negative acceleration — the velocity keeps decreasing.
Sloping line → the acceleration itself is changing.
The big idea: The area between an acceleration–time (a–t) graph and the time axis gives the change in velocity, Δv.
Area above the time axis → a positive change in velocity (+Δv).
Area below the time axis → a negative change in velocity (−Δv).
Overall Δv = area above − area below.
Final velocity = initial velocity + overall Δv.
Animated graph
Watch the graph build step by step in study mode.
For the a–t graph above, the area above the axis is 8 m s⁻¹ and the area below the axis is 2 m s⁻¹. The object starts from rest. Find its final velocity.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
What happens when the a–t graph crosses the time axis?: When the line crosses the time axis, the acceleration is zero at that instant and then changes direction. It does not mean the object has stopped.
Acceleration describes how the velocity is changing — it is not the velocity itself.
| What it means | |
|---|---|
| Acceleration = 0 | The velocity stays constant at that instant — the object may still be moving quickly. |
| Velocity = 0 | The object is momentarily not moving. |
Never wonder what to study next
Get a personalized daily plan based on your exam date, progress, and weak areas. We'll tell you exactly what to review each day.
What we're doing: We'll read a skydiver's acceleration–time graph: they speed up as they fall, then slow down when the parachute opens.
a = 0 does not mean stopped: When a = 0 the skydiver has only stopped speeding up — they keep falling at a steady speed.
Acceleration tells you how the speed is changing, not whether the skydiver is moving.
Animated graph
Watch the graph build step by step in study mode.
A skydiver falls, then opens a parachute. Its a–t graph has one area above the axis and one below.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.