Graphs of Motion · Form 4
Graphs of Motion: Key Terms
The key Graphs of Motion terms you need for SPM Mathematics, defined plainly in English, Malay and Chinese.
- Distance–time graph A graph showing distance against time; its gradient gives the speed.
- Speed–time graph A graph of speed against time; its gradient gives acceleration and the area beneath gives distance.
- Gradient How steep a line is; the rate of change of the vertical axis with respect to the horizontal.
- Acceleration The rate of change of speed, read as the gradient of a speed–time graph.
- Average speed Total distance divided by total time over a journey.
- Uniform velocity Motion at a constant speed in a fixed direction, shown as a straight line on a distance–time graph.
Term pairs students mix up
- Distance-time graph vs speed-time graph. The difference is: on a distance-time graph the gradient is speed, while on a speed-time graph the gradient is acceleration and the area is distance.
- Speed vs velocity. The difference is: speed is size only, while velocity is speed together with a direction, so uniform velocity means a steady speed in a fixed direction.
- Acceleration vs deceleration. The difference is: both are the gradient of a speed-time graph, but deceleration is simply a negative acceleration, meaning the object slows down.
- Average speed vs uniform speed. The difference is: uniform speed is one steady value shown as a flat line on a speed-time graph, while average speed is total distance divided by total time over the whole journey.
- Gradient vs area. The difference is: the gradient gives a rate such as speed or acceleration, while the area gives an accumulated amount, namely the distance travelled.
How these terms appear in a real SPM question
- The graph shows the speed, in m/s, of a particle tells you the vertical axis is speed, so gradient means acceleration and area means distance.
- Find the rate of change of speed is asking for acceleration, which is the gradient of that stage.
- Find the distance travelled or the total distance means find the area under the speed-time graph.
- Moves with uniform velocity signals a horizontal line on the speed-time graph, so the acceleration for that stage is zero.
- Comes to rest or starts from rest fixes a speed of 0 m/s at that point, giving you a coordinate to work from.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Does retardation mean the same as deceleration in SPM questions?
Yes. Retardation, deceleration and negative acceleration all describe the same thing, an object slowing down.
The gradient of the speed-time graph is negative in that stage. If a question asks for the retardation as a value, give the positive size, but if it asks for the acceleration, keep the negative sign.
When a question says velocity but the graph is labelled speed, does it matter?
For SPM motion in a straight line, treat the numbers the same way: the gradient still gives acceleration and the area still gives distance. The word velocity carries a direction, but the working on the graph is identical.
Just answer using whichever word the question uses, and keep your units consistent.
What does uniform actually signal when I see it in a motion question?
Uniform means constant, but read what it applies to. Uniform velocity or uniform speed means a steady speed, so a flat line on a speed-time graph with zero acceleration.
Uniform acceleration means the acceleration is constant, so a straight sloping line on a speed-time graph. The word tells you the graph is made of straight segments.