A DISTANCE–TIME GRAPH shows distance from a reference point (y-axis) against time (x-axis).
GRADIENT = SPEED:
Steeper gradient → faster speed.
Flat (horizontal) line → stationary (speed = 0).
Downward slope → returning towards start.
UNIFORM MOTION (constant speed): straight line with constant gradient.
NON-UNIFORM MOTION (changing speed): curved line — gradient changes.
CALCULATING SPEED FROM GRADIENT:
speed = Δd ÷ Δt = (change in distance) ÷ (change in time)
Pick two clear points on the line and divide the vertical change by the horizontal change.
Different Motion Shapes
STATIONARY: horizontal straight line (distance doesn't change).
CONSTANT SPEED: straight line with positive gradient.
ACCELERATING: curve with increasing gradient (getting steeper).
DECELERATING: curve with decreasing gradient (getting shallower).
RETURNING: line going back down — distance from starting point decreasing.
EXAMPLE:
Graph shows: 0–4 s: straight line to 20 m (constant speed).
4–6 s: horizontal (stationary).
6–10 s: straight line back to 0 m.
Speed in first section: 20 m ÷ 4 s = 5 m/s
Speed stationary: 0 m/s
Return speed: 20 m ÷ 4 s = 5 m/s
Using the Graph
EXAM TECHNIQUE:
Always use a large triangle when calculating gradient — minimises reading errors.
Read coordinates from the axis, not from the line itself if possible.
Check units — distance in metres, time in seconds → speed in m/s.
TANGENT TRICK (Higher Tier):
For a curved distance–time graph, draw a tangent at the point of interest.
Gradient of tangent = instantaneous speed at that point.
FOUNDATION LEVEL:
Only need to find average speed from a straight-line section.
Describe the motion from different sections of the graph.
⚠️ Common Mistake
A FLAT (horizontal) section means the object is STATIONARY — not moving at constant speed. Constant speed gives a diagonal straight line. A steeper line means FASTER speed.
📐 Variables
vSpeed (v) is measured in m/s (m/s)
dDistance (d) is measured in metres (m)
tTime (t) is measured in seconds (s)
📐 Key Equations
Speed = gradient of distance–time graph = Δd ÷ Δt
📌 Key Note
Gradient of d–t graph = speed. Steep straight line = fast constant speed. Flat line = stationary. Curve = changing speed (accelerating or decelerating). Negative gradient = returning to start. Calculate speed: pick two points, speed = Δd/Δt.
Match each section of a d–t graph to the motion it represents. — drag the symbols on the right to match the component names on the left.
Steep straight line upward
Drop here
Horizontal flat line
Drop here
Gentle straight line upward
Drop here
Straight line downward
Drop here
Upward curve (increasing steepness)
Drop here
Stationary — object has stopped
Constant speed returning towards starting point
Slow constant speed away from start
Fast constant speed away from start
Accelerating — speed increasing over time
⚽ FIFA Worked Examples
Speed from d–t Graph
A d–t graph shows an object moving from 0 m to 60 m in the first 12 seconds. Calculate the speed.
F
Speed = gradient = Δd ÷ Δt
I
Δd = 60 − 0 = 60 m, Δt = 12 − 0 = 12 s
F
Speed = 60 ÷ 12
A
Speed = 5 m/s
⭐ Higher Tier Only
Calculate the instantaneous speed of an accelerating object at a specific time by drawing a tangent to the curve at that point on a distance–time graph and calculating its gradient. Distinguish between instantaneous and average speed.
🎯 Test Yourself
Question 1 of 2
1. A d–t graph shows a horizontal (flat) line for 5 seconds. What is the object doing?
2. On a distance–time graph, two straight sections are drawn. Section A has gradient 8 m/s and section B has gradient 2 m/s. Which section shows faster motion?
⭐ How Well Do You Understand This Topic?
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