Motion
Speed, velocity and acceleration, distance–time and speed–time graphs, and motion under gravity.
Review these first
Learning objectives
What you need to be able to do
Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.
- 1.2.1Define speed as distance travelled per unit time and calculate it using v = s / t.
- 1.2.2Define velocity as speed in a given direction, and acceleration as change of velocity per unit time.
- 1.2.3Interpret distance–time and speed–time graphs, including gradient and area.
- 1.2.4Describe the motion of objects falling with and without air resistance, including terminal velocity.Supplement
8 minute read
Speed, velocity and acceleration
The three quantities
Speed is how much distance is covered per second: v = s / t, measured in m/s.
Velocity is speed in a stated direction. A velocity of −5 m/s means 5 m/s in the negative direction.
Acceleration is how quickly velocity changes: a = Δv / t, measured in m/s². A negative acceleration (deceleration) means the object is slowing down, or speeding up in the negative direction — read the question carefully.
Reading graphs
This is where most marks are won and lost.
On a distance–time graph:
- a horizontal line means stationary
- a straight sloping line means constant speed
- the gradient is the speed
- a curve means the speed is changing
On a speed–time graph:
- a horizontal line means constant speed
- the gradient is the acceleration
- the area under the line is the distance travelled
That last point is worth memorising as a single sentence: gradient gives acceleration, area gives distance.
Falling objects
Near the Earth's surface, an object in free fall accelerates at about 9.8 m/s² (often taken as 10 m/s² in calculations).
With air resistance, the story changes:
- At the start, speed is zero, so air resistance is zero and acceleration is maximum.
- As the object speeds up, air resistance grows.
- When air resistance equals weight, the resultant force is zero, so acceleration is zero.
- The object then falls at a constant terminal velocity.
Note that it keeps falling — it does not stop. Terminal velocity means constant speed, not zero speed.
Think of it like this
A speed–time graph is like a bank statement of motion: the height tells you the current rate, and the area you have "accumulated" tells you the total distance.
Worked examples
Method, step by step
A car accelerates uniformly from rest to 24 m/s in 8.0 s. Calculate the acceleration and the distance travelled.
- 1Acceleration: a = Δv / t = (24 − 0) / 8.0 = 3.0 m/s²
- 2Distance = area under the speed–time graph = ½ × base × height
- 3Distance = ½ × 8.0 × 24 = 96 m
a = 3.0 m/s², s = 96 m
A cyclist travels 450 m in 30 s. Calculate the average speed.
- 1v = s / t
- 2v = 450 / 30
v = 15 m/s
Common misconceptions
- Reading a distance–time graph as if it were a speed–time graph. A horizontal line on the first means "not moving"; on the second it means "moving at a steady speed".
- Believing that at terminal velocity the object stops falling. It falls at a constant speed because the resultant force is zero.
- Assuming heavier objects always fall faster. Without air resistance they accelerate identically.
In the exam
- For "describe the motion" questions, work through the graph section by section and use the words: constant speed, accelerating, decelerating, stationary.
- When finding distance from a speed–time graph, split the area into triangles and rectangles and show each area separately.
- Always state the direction when a question asks for velocity rather than speed.