Introduction
Graphical kinematics is one of the most reliable sources of marks in the 9709 Mechanics paper. Rather than computing algebraically, questions ask you to read, sketch, and interpret two types of motion graph. A firm understanding of what gradient and area mean on each graph type allows you to extract every kinematic quantity — displacement, velocity, and acceleration — directly from the picture.
Core Concept
Two graph types capture all one-dimensional motion:
Displacement–time (s–t) graph — the vertical axis shows displacement from a fixed origin; the horizontal axis shows time .
Velocity–time (v–t) graph — the vertical axis shows velocity ; the horizontal axis shows time .
Three fundamental interpretations connect these graphs:
| Graph | What the gradient gives | What the area gives |
|---|---|---|
| Displacement–time ( vs ) | Velocity | — (not directly used) |
| Velocity–time ( vs ) | Acceleration | Displacement (signed) |
These follow directly from the definitions and , which you met in the prerequisite topic.
Displacement–Time Graphs — Key Features
- A positive gradient means the object moves in the positive direction.
- A negative gradient means the object moves in the negative direction.
- A zero gradient (horizontal line) means the object is stationary.
- A curved section means the velocity is changing (non-uniform motion).
- The steeper the line, the greater the speed.
Velocity–Time Graphs — Key Features
- A positive gradient means positive acceleration (speeding up in positive direction, or slowing down in negative direction).
- A negative gradient means negative acceleration (deceleration when moving in the positive direction).
- A zero gradient (horizontal line) means constant velocity.
- Area above the -axis contributes positive displacement; area below contributes negative displacement.
- Total distance = sum of the absolute values of all areas (regardless of sign).
Unlock the full Kinematics of Motion in a Straight Line note with Nova
You're reading the preview. Unlock the complete note — every worked example, examiner pitfall and practice question — plus 24/7 AI tutoring from Nova that teaches directly from these notes.