IGCSE Physics (0625)

Speed-time graphs

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

The maximum speed on a speed–time graph is the highest value reached on the vertical (speed) axis, not the total distance or the duration.
Common mistake: Students often confuse the flat section's length with speed instead of reading its height.
A straight line through the origin on a speed–time graph means constant (uniform) acceleration from rest, so the cyclist's speed increases by equal amounts in equal time intervals.
Common mistake: Students often miss this if they only look at the speed values, not the graph's shape.
For motion with uniform acceleration from rest, the speed at any time is proportional to the elapsed time, so at half the total time to a given speed, the speed is half as much.
Common mistake: Students often forget this proportionality and do not scale correctly.
For a fixed distance, a longer journey time means the tram must have spent time at a lower speed somewhere (e.g., lower cruising speed or more time stopped), not just decelerated briefly or accelerated more slowly.
To find distance from a speed–time graph, calculate the area under the line (here, a triangle).
Common mistake: A common mistake is to multiply speed by time directly, ignoring that speed is changing and not constant.
To find distance from a speed–time graph, sum the areas under the graph (including triangles and rectangles).
Common mistake: A common mistake is to use the gradient (which gives acceleration) or to ignore the need to split the shape.

State the maximum speed of the cable car.

Try it first, then show the working

Answer: 12 m/s

19 exam-style questions on Speed-time graphs, each marked to the scheme.