Velocity-time Graphs — Movement & Position | IGCSE Physics

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 12% of your exam marks.

stable

High

Stable12%

Distance-time graphs, speed calculations and velocity appear in nearly every series.

Reading the slope

A velocity-time graph plots an object's velocity (y-axis) against the time elapsed since the start of the motion (x-axis)
The slope of the line tells you about the acceleration:
- A straight line with a positive gradient means constant acceleration, with velocity climbing at a steady rate
- A straight line with a negative gradient means constant deceleration, with velocity falling at a steady rate
- A steep line signals a large magnitude of acceleration; a gentle line signals a small one
- A flat horizontal line means zero acceleration, so the velocity stays at a single fixed value (a constant velocity)

A velocity-time graph showing three labelled straight lines on the same axes — one rising (constant acceleration), one falling (constant deceleration), one horizontal (constant velocity) — with a gradient triangle drawn on the rising section

Gradient = acceleration

The acceleration of an object equals the gradient of its velocity-time graph:

a = Δy / Δx = Δv / Δt

For a straight-line section, the gradient is the same everywhere, so draw a large gradient triangle and divide the rise by the run, taking care to read the axes in their stated units (m/s and s)

Example — between t = 0 s and t = 4.0 s, a cyclist's velocity rises in a straight line on a v-t graph from 0 to 8.0 m/s. Calculate the cyclist's acceleration.

Δv = 8.0 − 0 = 8.0 m/s; Δt = 4.0 s
a = Δv / Δt = 8.0 / 4.0 = 2.0 m/s²