Sheet № 198 · Foundation + Higher · AQA · Edexcel · OCR
Velocity-Time Graphs –
Velocity-time graphs are tested on both Foundation and Higher GCSE Maths papers and link algebra, geometry, and real-world problem solving. Understanding how to read and interpret them is essential for questions involving speed, acceleration, and distance.
§Key definitions
Question:
A car accelerates from rest to 20 m/s in 10 seconds, then travels at constant speed for 15 seconds. Find the total distance.
Answer:
400 metres
Q1 (Foundation):
An object accelerates from rest to 30 m/s in 6 seconds. Find the acceleration.
Q2 (Foundation):
A train travels at 40 m/s for 20 seconds. Find the distance covered.
Q3 (Higher):
A car accelerates from 10 m/s to 25 m/s in 6 seconds, then decelerates to rest in 10 seconds. Find the total distance.
§Formulas to memorise
Acceleration = gradient = change in velocity / change in time
Distance = area under the velocity-time graph
Area of triangle = ½ × base × height, Area of trapezium = ½ × (a + b) × h
To find acceleration, calculate the gradient of the relevant section: rise / run = change in velocity / change in time.
Worked example
A car accelerates from rest to 20 m/s in 10 seconds, then travels at constant speed for 15 seconds. Find the total distance.
Working:
⚠ Common mistakes
- ✗Confusing velocity-time graphs with distance-time graphs. On a velocity-time graph, a horizontal line means constant speed, not being stationary. On a distance-time graph, a horizontal line means stationary.
- ✗Forgetting to halve the area for triangular sections. A triangular section is ½ × base × height, not base × height.
- ✗Using the wrong units. Acceleration is measured in m/s² (metres per second squared), not m/s.
✦ Exam tips
- →Label each section of the graph (acceleration, constant speed, deceleration) before calculating.
- →Use a trapezium when the graph goes from one velocity to a different velocity over a time period — area = ½ × (v₁ + v₂) × t.
- →If the question asks for deceleration, give a positive value. Deceleration is the magnitude of negative acceleration.