Graphs of Motion · Form 4
What does gradient mean on a motion graph?
Gradient is the steepness of the line, and on a motion graph steepness always means a rate, but which rate depends on the graph: speed on a distance–time graph, acceleration on a speed–time graph.
Gradient is a rate of change
Gradient is the change up the vertical axis divided by the change along the horizontal axis. On a motion graph the vertical axis is distance or speed and the horizontal axis is time, so the gradient is a change per unit of time, that is, a rate.
This is why a steeper line always means a faster rate.
Same steepness, different meaning
On a distance–time graph the gradient is distance ÷ time, which is speed. On a speed–time graph the gradient is speed ÷ time, which is acceleration.
So you must know which graph you are looking at before you name its gradient: a flat line means stationary on a distance–time graph, but constant speed on a speed–time graph.
The usual mistake
Many students read the gradient's number without its units and assume a steep line always means 'fast'. The meaning comes entirely from the axes: the same steep line means high speed on one graph and large acceleration on another.
A negative gradient means decreasing, returning on a distance–time graph, or decelerating on a speed–time graph, not a negative speed.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I actually calculate the gradient of a section on a motion graph?
Take two clear points on that straight section, find the change in the vertical value divided by the change in the horizontal value (rise over run), matching the units on each axis. On a distance-time graph this gives speed in units like m/s, while on a speed-time graph it gives acceleration in units like m/s².
Why does the same word 'gradient' mean speed on one graph and acceleration on another?
Gradient always measures how fast the vertical quantity changes with time, but that quantity differs on each graph, distance on a distance-time graph, speed on a speed-time graph. Since speed is the rate of change of distance and acceleration is the rate of change of speed, the gradient naturally represents whichever rate matches the graph.
What is a common mistake when working with gradient on motion graphs?
A frequent error is treating a negative gradient as a "negative speed", when it actually means the object is decelerating on a speed-time graph or moving back towards the start on a distance-time graph. Always state what the negative sign means in context rather than leaving a bare negative number as the final answer.