Acceleration and speed-time graphs
This is Cambridge International IGCSE Physics 0625, separate from the Egyptian Baccalaureate / Thanaweya Amma and not a Year 3 course. Last lesson you read motion graphs. Now you will use their areas to find distance. The book marks acceleration calculations and graph gradients as Supplement / Extended only, so those parts are clearly labelled.
A speed-time graph can tell you distance
Time runs along the bottom; speed is read up the side. For a short time interval, distance = speed × time. On this graph that multiplication is the area between the line and the time axis. So the area under a speed-time graph represents the distance travelled.
Open the worked example
A toy car travels at 6 m/s for 10 s. The graph makes a rectangle: width = 10 s and height = 6 m/s. Area = 10 × 6 = 60 m. The units work too: seconds × metres per second = metres.
Quick check: A runner moves at 4 m/s for 8 s. What is the area under the flat graph line, and what does it mean?
Think, then reveal: Area = 4 × 8 = 32 m. The area means the runner travelled 32 m.
See what the graph’s area and gradient mean
Explore the area under a speed-time graph
Choose a journey. Before opening the working, predict the distance from the shape underneath the line.
Total distance = 900 m
Reveal the area calculations
- First triangle: ½ × 10 s × 20 m/s = 100 m
- Rectangle: 30 s × 20 m/s = 600 m
- Last triangle: ½ × 20 s × 20 m/s = 200 m
Add them: 100 + 600 + 200 = 900 m.
Explore acceleration (Supplement / Extended only)
Adjust the starting speed, final speed and time. Notice that braking makes final speed smaller, so the calculated acceleration is negative.
a = (v − u) ÷ t = (17 − 5) ÷ 4 = 3.00 m/s²
Practise, then read the explanation
Questions marked Supplement / Extended use the extra acceleration ideas. Try the question first, open the optional hint if you need help, then submit for the worked reasoning.
Optional hint
For a horizontal speed-time line, the area is a rectangle: base × height.
This original interactive lesson and practice set align to Cambridge IGCSE Physics 0625 syllabus links 1.2.4, 1.2.5, 1.2.7 and 1.2.9–1.2.12 as identified in Volume A, Lesson 4. Core speed-time graph interpretation and area questions are separated from Supplement / Extended acceleration calculations, gradients, negative acceleration and changing-acceleration graphs. Source reading: Physics-0625 Volume A, PDF pp. 27–32 (printed pp. 19–24).