CAIE 0625 IGCSE•Topic 1.2.2•Reading Time: 6 mins•Author: IGCSE Physics Tutor

1.2.2 Distance-Time Graphs & Determining Speed

Learn to read the shape of a distance-time graph, pull a numerical speed out of its gradient, and tell constant speed apart from acceleration without needing a single equation of motion.

1. The Meaning of Gradient

A distance-time graph plots how far an object has travelled (vertical axis) against time elapsed (horizontal axis). Almost every question on this graph type is really asking you to read the slope correctly.

Fundamental Postulate

The gradient of a distance-time graph at any point gives the speed of the object at that instant. A steeper line means a greater speed; a flat, horizontal section means the object is stationary (speed=0\text{speed} = 0).

FIGURE 1.2.2A: Three Phases of a Journey on a Distance-Time Graph
distance (d)time (t)A: at restB: constant speedC: acceleratingtangent = instantaneous speedΔtΔd
Notice: Section A is flat (at rest), Section B is a straight incline (constant speed), and Section C curves upward and steepens — the tangent drawn at the end of C gives the instantaneous speed at that moment.

2. Reading Graph Shape as Physical Motion

Graph FeatureMeaningHow to Find the Speed
Horizontal lineObject is stationaryspeed=0\text{speed} = 0
Straight sloped lineConstant speedspeed=ΔdΔt\text{speed} = \dfrac{\Delta d}{\Delta t} using any two points on the line
Curve getting steeperAccelerating (speeding up)speed=\text{speed} = gradient of the tangent at that instant
Curve getting less steepDecelerating (slowing down)gradient of the tangent, decreasing over time
Exam Tip — Common IGCSE Trap

Common IGCSE trap: students read off how high up the graph is at a point and think that is the speed. The height of the graph is the total distance travelled so far, NOT the speed. Speed always comes from the slope, never the height.

WORKED EXAMPLEFinding Average Speed from a Distance-Time Graph
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Up Next: 1.2.3 Graphical Analysis: Velocity-Time Graphs