A Level Maths: Displacement-Time and Velocity-Time Graphs Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Kinematics (Velocity and Displacement Time Graphs) (OCR)
- Kinematics (Velocity and Displacement Time Graphs) (Edexcel)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Straight Line Geometry — gradient is fundamental to reading these graphs
- GCSE Maths Graphs — reading values from coordinate graphs is assumed
- Integration — needed for area under curved velocity-time graphs
A Level Maths displacement-time and velocity-time graphs is the visual side of kinematics in the Mechanics strand. You read and draw these graphs, extract information from them (gradient and area), and use them to solve problems about motion in a straight line. This skill set runs through Kinematics: Constant Acceleration (SUVAT) and Kinematics: Variable Acceleration.
For a displacement-time graph, the gradient at any point is the velocity at that moment. Stationary objects appear as horizontal lines; objects moving at constant velocity appear as straight lines with constant gradient; accelerating objects appear as curves. For a velocity-time graph, the gradient is the acceleration, and the AREA under the graph (between the curve and the time axis) is the displacement. You read off displacement, velocity, and acceleration from these graphs, solve problems involving multiple stages of motion (acceleration, constant speed, deceleration), and switch between the two graph types to solve real-world problems.
Displacement-time and velocity-time graphs are part of the Mechanics strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: distance and displacement are DIFFERENT — displacement can be negative, distance cannot; the gradient of a displacement-time graph gives velocity (NOT acceleration); the area below the time axis on a velocity-time graph corresponds to negative displacement; and for curved velocity-time graphs, the area is found using Integration rather than simple geometry.