Overview
What you’ll learn
- State what is meant by speed and velocity, and calculate average speed as distance travelled over time taken.
- State what is meant by uniform acceleration and calculate it from the change in velocity over time taken; interpret non-uniform acceleration.
- Plot and interpret distance-time and speed-time graphs, deducing rest, uniform speed and uniform or non-uniform acceleration from their shapes.
- Calculate the area under a speed-time graph to find the distance travelled.
- State that the acceleration of free fall near the Earth is approximately 10 m/s².
Key points
- 1Speed = distance ÷ time (scalar); velocity = speed with a direction (vector).
- 2Average speed = total distance ÷ total time — the whole journey, not one stretch.
- 3Acceleration = change in velocity ÷ time taken, in m/s²; uniform means the velocity changes by equal amounts each second.
- 4Distance–time graph: gradient = speed. Flat = at rest; straight slope = steady speed; curve = changing speed.
- 5Speed–time graph: gradient = acceleration; area under the graph = distance travelled.
- 6Free fall: everything near Earth accelerates downwards at about g = 10 m/s² (ignoring air effects).
Notes · 1 of 5
Speed, velocity and average speed
Distance over time — with a direction when you need one.
Speed is how much distance is covered each second: speed = distance ÷ time, measured in m/s (or km/h). Velocity is the vector version — the same idea with a direction attached: 8 m/s north. For a journey with changing speed we quote the average speed: total distance travelled ÷ total time taken, including any stops.
Notes · 2 of 5
Acceleration
How quickly velocity changes — in m/s².
Acceleration is the rate of change of velocity: acceleration = change in velocity ÷ time taken = (v − u) ÷ t, measured in m/s². An acceleration of 3 m/s² means the velocity grows by 3 m/s every second. Uniform acceleration means equal velocity changes in equal times — a steady value on the calculation. Non-uniform acceleration means the rate itself changes: the velocity still changes, but by different amounts each second.
Deceleration (slowing down) is just acceleration with a negative sign when the positive direction is fixed: a car slowing from 20 m/s to rest in 5.0 s accelerates at (0 − 20) ÷ 5.0 = −4.0 m/s². Keep the signs tied to one chosen direction and the arithmetic looks after itself.
Notes · 3 of 5
Distance–time graphs
Gradient is the whole story.
On a distance–time graph (distance on the vertical axis, time horizontal), the gradient is the speed. The three shapes to recognise: a horizontal line means the object is at rest (distance not changing); a straight sloping line means steady (uniform) speed; a curve means the speed is changing — steepening means speeding up, levelling off means slowing down.
| Shape | Meaning |
|---|---|
| horizontal line | at rest — zero speed |
| straight slope up | constant speed (gradient = speed) |
| curve getting steeper | speeding up (accelerating) |
| curve levelling off | slowing down (decelerating) |
To compare speeds from a graph, compare gradients: the steeper line is the faster object — no calculation needed. For a curved section, the speed at one moment is the gradient of the curve at that point (how steep it is there), which you describe as steepening or levelling rather than compute.
Notes · 4 of 5
Speed–time graphs
Gradient is acceleration; area is distance.
On a speed–time graph, the gradient is the acceleration: a straight rising line is uniform acceleration, a horizontal line is constant speed, a straight falling line is uniform deceleration, and a curve signals non-uniform acceleration. The second power of this graph: the area between the line and the time axis equals the distance travelled.
Notes · 5 of 5
Free fall and g
Everything falls with the same acceleration — about 10 m/s².
Drop something and its velocity changes by about 10 m/s every second — the acceleration of free fall, g ≈ 10 m/s² near the Earth, pointing downwards. After 1 s a dropped object falls at about 10 m/s; after 2 s, about 20 m/s; after 3 s, about 30 m/s. In this course we treat free fall as uniform acceleration — the same graph rules apply, with the speed–time line rising straight and the distance coming from the area.
Revise
Key terms
The words examiners expect you to use precisely.
- speed
- Distance travelled per unit time — a scalar.Calculated as distance ÷ time, in m/s.
- velocity
- Speed in a stated direction — a vector.Same number as speed on a straight route, but with a direction attached.
- average speed
- Total distance travelled divided by total time taken.Stops count in the time even though they add no distance.
- acceleration
- The rate of change of velocity: (v − u) ÷ t, in m/s².Uniform acceleration changes velocity by equal amounts each second.
- uniform acceleration
- Acceleration that stays constant — equal velocity changes in equal times.A straight line on a speed–time graph.
- deceleration
- Acceleration in the direction opposite to the motion — the object slows down.Appears as a negative acceleration or a downward line on a speed–time graph.
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- acceleration of free fall
- The downward acceleration of a freely falling object near the Earth, about 10 m/s².Quoted as g = 10 m/s² in this course.
- area under a speed-time graph
- The distance travelled during the time shown.Split into triangles and rectangles, then add the areas.
Revise
Common mistakes
Where students most often lose marks in this chapter — and what to do instead.
Mistake: Computing average speed from one stretch of a journey.
Average speed is defined over the whole trip.
Instead: Average speed = total distance ÷ total time, including rests.
Mistake: Writing acceleration in m/s.
Acceleration is a change of speed per second — two time powers.
Instead: Acceleration units are m/s²: metres per second, every second.
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Mistake: Reading a flat line on a distance–time graph as constant speed.
Flat means the distance is not changing at all.
Instead: Flat on a distance–time graph = at rest; constant speed = straight slope.
Mistake: Calling a steepening curve "constant speed".
A changing gradient means a changing speed.
Instead: Steepening = speeding up; levelling = slowing down — only straight lines have constant gradient.
Mistake: Confusing the gradient and the area on a speed–time graph.
They answer different questions.
Instead: Gradient = acceleration; area = distance.
Mistake: Finding distance by multiplying final speed by total time.
That ignores the speeding-up and slowing-down stages.
Instead: Split the area under the graph into triangles and rectangles and add.
Mistake: Forgetting the ½ in a triangle area.
The triangle is half the matching rectangle.
Instead: Triangle area = ½ × base × height.
Mistake: Dropping the negative sign for deceleration.
Slowing from 20 m/s to 0 is a change of −20 m/s.
Instead: Fix a positive direction and keep signs: (0 − 20) ÷ 5.0 = −4.0 m/s².
Mistake: Using 9.8 or 9.81 for g in this course.
The Combined data treatment rounds free fall to one significant figure.
Instead: Use g = 10 m/s² exactly as the syllabus states.
Mistake: Saying heavier objects fall with bigger acceleration.
Free-fall acceleration is the same for all objects near Earth (this course ignores air effects).
Instead: Everything accelerates downwards at about 10 m/s² regardless of mass.
Mistake: Quoting speed without units.
A number alone is not a speed.
Instead: Speed in m/s (or km/h), acceleration in m/s² — units travel with every answer.
Mistake: Reading a distance–time graph backwards.
Axes decide meaning; the shape alone does not.
Instead: Check the vertical axis first: distance → gradient is speed; speed → gradient is acceleration.
Check yourself
Quick quiz
20 questions with instant explanations. About 5 minutes.
Question 1 of 3
- Question 1: current question
- Question 2: not answered
- Question 3: not answered
State what is meant by speed and velocity, and calculate average speed as distance travelled over time taken.
A jogger covers 600 m in 300 s. Her average speed is
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Practise
Topical questions
Exam-style practice in three tiers, from recall to data questions.
- 4Foundation
- 3Standard
- 5Challenging
12 questions worth 63 marks, each with a model answer, mark scheme and examiner tips.
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Exam practice
Practice paper
A 30-mark paper set out like a school paper, with a separate mark scheme. Give yourself 40 min.
Question paper
Chapter 2 Practice Paper
30 marks · 40 min · 5 pages
5 multiple-choice questions and structured questions with answer lines. Chapter 2 (speed and velocity, average speed, acceleration, distance-time and speed-time graphs, free fall).
Mark scheme
PROChapter 2 Practice Paper — mark scheme
Answers · Marking points · 3 pages
Model answers with a mark for each creditworthy point — for marking at home or in class.
Where this chapter is tested
Each school sets its own scope — check your assessment outline.
Questions
Frequently asked questions
What is the difference between speed and velocity again?
Speed is distance over time — a plain number. Velocity is speed with a direction: 8 m/s north. On a straight route the numbers match; the direction is what makes velocity a vector.
How do I read a speed–time graph quickly?
Two questions: how steep (gradient = acceleration) and how much area (area = distance). Flat means constant speed; rising means speeding up; falling means slowing down.
Why does the area under a speed–time graph give distance?
Because distance = speed × time. Each thin strip of the graph has height (speed) × width (time) = a little distance; adding all strips gives the whole distance.
Do heavier things fall faster?
Not in this model: free fall near Earth accelerates everything at about 10 m/s² regardless of mass. Air effects are ignored in Combined Science calculations.