Kinematics and Motion Graphs

This guide covers subtopic 1.2 Motion, with the scalar/vector distinction from 1.1, from Topic 1, Motion, forces and energy, for Cambridge O Level Physics 5054, 2026–2028 series.

Where this fits in 5054

Kinematics — describing how things move, without yet asking what forces cause that motion — is the foundation Topic 1 is built on. The vocabulary here (speed, velocity, acceleration) and the graph-reading skills carry straight into Forces and Motion (1.5), where F = ma connects motion to the forces that produce it, and into Momentum (1.6), which is built directly from velocity. The measurement techniques half of subtopic 1.1 — how length, volume and time are actually measured — is covered in Measurement, Mass, Weight and Density.

A note on scope. This page is written against Cambridge O Level Physics 5054, which is not tiered. Cambridge IGCSE Physics 0625 covers motion under the same topic structure but is tiered Core/Extended — check your own syllabus document if you’re studying 0625, since outcome depth can differ between the two qualifications even where topic names match.

Syllabus coverage

CAMBRIDGE O LEVEL PHYSICS 5054

• Understand that a scalar quantity has magnitude only, and a vector quantity has magnitude and direction (1.1)
• Know that distance, speed, time, mass, energy and temperature are scalars; displacement, force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength are vectors (1.1)
• Define speed as distance travelled per unit time, and velocity as change in displacement per unit time (1.2)
• Recall and use speed = distance ÷ time, and average speed = total distance ÷ total time (1.2)
• Define acceleration as change in velocity per unit time; recall and use acceleration = change in velocity ÷ time taken (1.2)
• Describe uniform and non-uniform acceleration, and know that deceleration is a negative acceleration (1.2)
• Sketch, plot and interpret distance–time and speed–time graphs, including calculating speed from a distance–time gradient, acceleration from a speed–time gradient, and distance from the area under a speed–time graph (1.2)
• State that the acceleration of free fall, g, is approximately 9.8 m/s² near the Earth’s surface (1.2)

5054 is not tiered — every candidate covers all of the above.

Scalars and vectors

A scalar quantity has size only — 5 metres, 20 seconds, 70 kg. A vector quantity has size and direction — “5 metres north” is a displacement; “5 metres” on its own, with no direction, is just a distance.

Scalar (magnitude only)	Vector (magnitude + direction)
distance	displacement
speed	velocity
time, mass, energy, temperature	acceleration, force, weight, momentum
	electric field strength, gravitational field strength

This distinction matters constantly in kinematics: distance is the total length of a path travelled, regardless of direction, while displacement is how far you end up from your starting point, in a straight line, with a direction attached. A runner completing one full lap of a 400 m track has travelled a distance of 400 m, but their displacement is zero — they’re back where they started.

Speed and velocity

Speed is distance travelled per unit time:

speed = distance / time        v = s / t

Where speed varies during a journey, average speed uses the totals:

average speed = total distance travelled / total time taken

Velocity is the vector version — change in displacement per unit time, in a stated direction. Two objects can have the same speed but different velocities if they’re moving in different directions.

Worked example. A car travels 150 m in 12 s. What is its average speed?

average speed = 150 / 12 = 12.5 m/s

Acceleration

Acceleration is the change in velocity per unit time:

acceleration = change in velocity / time taken        a = Δv / Δt

Acceleration is uniform if velocity changes by equal amounts in equal time intervals, and non-uniform otherwise. A deceleration is simply a negative acceleration — an object slowing down — and should be treated as a negative value in calculations rather than as a separate quantity.

Worked example. A cyclist accelerates from 2 m/s to 8 m/s in 4 s. Find the acceleration.

a = Δv / Δt = (8 − 2) / 4 = 6 / 4 = 1.5 m/s²

Worked example. A trolley decelerates from 12 m/s to 4 m/s in 2 s. Find the acceleration.

a = Δv / Δt = (4 − 12) / 2 = −8 / 2 = −4 m/s²

The negative sign shows this is a deceleration of 4 m/s².

Distance–time graphs

On a distance–time graph, what the line looks like tells you the motion directly:

• Flat (horizontal) line — the object is at rest.
• Straight line, sloping up — moving at constant speed.
• Curve getting steeper — accelerating.
• Curve getting less steep — decelerating.

The gradient of a distance–time graph gives the speed:

speed = gradient = change in distance / change in time

For a curved section, the gradient (and therefore the speed) at any instant is the gradient of the tangent to the curve at that point.

Speed–time graphs

A speed–time graph carries different information from the same-shaped lines:

• Horizontal line lying on the time axis (speed = 0) — the object is at rest.
• Flat (horizontal) line above the time axis — constant speed (zero acceleration).
• Straight line, sloping up — constant acceleration.
• Curve — changing acceleration.

Two calculations come from a speed–time graph:

gradient of speed–time graph = acceleration
area under speed–time graph = distance travelled

The area rule holds for motion at constant speed (a rectangle) or constant acceleration (a triangle, or a trapezium for an initial speed that isn’t zero) — split the graph into simple shapes and add the areas together.

Worked example. An object accelerates uniformly from rest to 10 m/s in 5 s, then travels at 10 m/s for a further 8 s. Find the total distance travelled.

Stage 1 (triangle): distance = ½ × base × height = ½ × 5 × 10 = 25 m
Stage 2 (rectangle): distance = base × height = 8 × 10 = 80 m

total distance = 25 + 80 = 105 m

The same figure, read as a distance–time graph instead, would show a curve steepening into a straight line — the same motion, described the other way.

Free fall

Near the Earth’s surface, an object falling freely has an acceleration of free fall, g ≈ 9.8 m/s², directed downward. This is a specific, recallable value, not something to derive — and it’s an acceleration, which is why it applies the vector/scalar distinction from earlier: g has both a size (9.8 m/s²) and a direction (downward).

Common mistakes

• Confusing distance and displacement, or speed and velocity. Distance and speed are scalars (size only); displacement and velocity are vectors (size and direction) — a return journey can have real distance/speed but zero net displacement/velocity.
• Reading a distance–time graph as if it were a speed–time graph. A straight sloping line means constant speed on a distance–time graph, but constant acceleration on a speed–time graph — the same shape means something different depending on which graph you’re looking at.
• Forgetting the area-under-the-graph rule only applies to speed–time graphs, not distance–time graphs — area under a distance–time graph isn’t a standard quantity in this syllabus.
• Treating deceleration as if it needs a different formula. It doesn’t — it’s the same acceleration equation, giving a negative value.
• Mixing up which axis a gradient is taken from. Always double-check whether the graph in front of you plots distance or speed on the vertical axis before deciding what a gradient or an area actually represents.

Quick revision checklist

• Scalar vs vector: which quantities are which, and why it matters for distance/displacement and speed/velocity
• Speed and average speed: definitions and the equation
• Acceleration: definition, equation, uniform vs non-uniform, deceleration as negative acceleration
• Reading motion from the shape of a distance–time graph and a speed–time graph
• Calculating speed from a distance–time gradient, acceleration from a speed–time gradient, and distance from the area under a speed–time graph
• g ≈ 9.8 m/s², the acceleration of free fall near the Earth’s surface

Related resources

• Measurement, Mass, Weight and Density — the rest of subtopic 1.1, plus 1.3 and 1.4
• Forces and Motion — Newton’s laws and F = ma, explaining why objects accelerate
• Momentum — mass and velocity combined into a single quantity, used throughout collisions and explosions questions
• Cambridge O Level Physics subject hub

Written against Cambridge O Level Physics 5054, 2026–2028 series. Always check the current syllabus for your examination year.