Graphs of Motion · 7.2.3
Interpreting speed-time graphs
Students read a speed-time graph and translate its shape into a description of real motion: a rising line means the object is accelerating, a horizontal line means constant speed, and a falling line means it is decelerating. They also calculate acceleration as the gradient, change in speed divided by change in time, of each section.
The official learning standard (7.2.3)
“Interpret speed-time graphs and describe the motion based on the graphs, involving distance, time, speed and acceleration, where acceleration is the change of speed with respect to time for a motion in a fixed direction.”
What it means
Students read a speed-time graph and translate its shape into a description of real motion: a rising line means the object is accelerating, a horizontal line means constant speed, and a falling line means it is decelerating. They also calculate acceleration as the gradient, change in speed divided by change in time, of each section.
How it is examined
This is tested in SPM Paper 2, usually as part of a structured question where students describe the motion in each stage of a given graph and calculate the acceleration or deceleration for a stated interval using gradient. Paper 1 may test a single gradient calculation from a simple graph.
Worked example
The graph shows the motion of a cyclist: speed increases uniformly from 0 m/s to 15 m/s during the first 3 seconds, stays constant at 15 m/s for the next 4 seconds, then decreases uniformly to 0 m/s during the last 2 seconds. (a) Describe the motion of the cyclist.
(b) Find the acceleration during the first 3 seconds.
- 0–3 s: speed rises from 0 to 15 m/s, so the cyclist is accelerating uniformly.
- 3–7 s: speed stays at 15 m/s, so the cyclist moves at constant speed.
- 7–9 s: speed falls from 15 to 0 m/s, so the cyclist is decelerating uniformly (braking).
- Acceleration in the first 3 s = (15 - 0) / 3 = 5 m/s².
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Is deceleration written as a negative acceleration?
Yes. If speed decreases from 15 m/s to 0 m/s in 2 s, acceleration = (0-15)/2 = -7.5 m/s².
The negative sign shows the object is slowing down; you can also describe this as a deceleration of 7.5 m/s².
Does a horizontal line always mean the object is not moving?
No, a horizontal line on a speed-time graph means the speed is constant, not necessarily zero. The object is still moving at that steady speed; it is only stationary if the line lies exactly on the time-axis, where speed equals zero.
How is acceleration different from speed on these graphs?
Speed is the value plotted on the vertical axis at any instant, while acceleration is the gradient of the graph, showing how quickly that speed is changing. A large gradient means speed changes quickly (high acceleration); a zero gradient means speed stays unchanged.