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.