Graphs of Motion · Form 4
How do you read a distance–time graph as a story?
A distance–time graph turns a journey into a picture: the shape of the line tells you when something is moving away, standing still, or coming back, before you calculate anything.
The picture of a journey
On a distance–time graph, time runs along the horizontal axis and distance from the starting point runs up the vertical axis. The height of the line at any moment answers just one question: how far from the start the object was right then.
Reading left to right is like watching the journey unfold over time.
Rising, flat and falling
A line sloping up means the distance is increasing, the object is moving away from the start. A flat, horizontal line means the distance is not changing, it is stationary, staying where it is.
A line sloping down means the distance is decreasing, the object is heading back towards the start, and a steeper slope means it is moving faster.
What a flat line does not mean
The most common misreading is thinking a flat line means the object has vanished or gone home, but a flat line high up on the graph means it is far away and staying there, at rest. Another slip is reading a downward slope as 'slowing down'; on a distance–time graph a downward slope means travelling back towards the start.
Direction of travel and speed are two different things on this graph.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How can I tell from the shape alone when an object is moving or standing still?
A sloping line means distance is changing, so the object is moving, while a flat horizontal segment means distance stays constant, so the object is stationary. Before calculating anything, scan the graph left to right and describe each segment in words, this quick read often answers part (a) of a Paper 2 question directly.
What does it mean when the line slopes back down towards the time axis?
A line sloping down means the distance from the starting point is decreasing, so the object is travelling back towards where it started. It does not mean time is going backwards, only that the object's position relative to the origin is now reducing, at a speed found from that section's gradient.
What mistake do students make when interpreting a distance-time graph?
A common error is assuming a steeper line always means a faster speed without checking the axes' scales, or reading distance and time values from the wrong axis. Always check both axis labels and units first, since two graphs can look equally steep but represent very different speeds if the scales differ.