Graphs of Motion · Form 4
Graphs of Motion: Revision Notes
A tight revision summary of Graphs of Motion for SPM Mathematics, the key ideas, the formulae the exam gives you, and what to focus on before the paper.
The big idea
This chapter connects graphs to movement. On a distance–time graph the gradient is speed; on a speed–time graph the gradient is acceleration and the area underneath is distance travelled.
You learn to draw these graphs, read values off them, and interpret what a shape says about a journey.
Key ideas to revise
- Gradient means rate. A steeper line means a faster rate, speed on a distance–time graph, acceleration on a speed–time graph.
- Area under a speed–time graph. The area beneath the line is the distance travelled, usually found by splitting it into triangles and rectangles.
- Reading a journey from the shape. A flat line means stationary; a downward slope on a distance graph means returning. The shape tells the story.
Every key idea as a quick worked example
- Gradient on a distance-time graph is speed: a line climbing from 0 m to 60 m in 4 s has gradient 60 divided by 4 = 15 m/s, so the object moves at 15 m/s.
- Gradient on a speed-time graph is acceleration: speed rising from 4 m/s to 16 m/s in 3 s gives (16 minus 4) divided by 3 = 4 m/s squared.
- Area under a speed-time graph is distance: a constant 12 m/s held for 5 s is a rectangle, 12 multiplied by 5 = 60 m.
- A triangular stage from rest to 10 m/s in 4 s has area one half multiplied by 4 multiplied by 10 = 20 m, the distance for that stage.
- The shape tells the story: a horizontal line on a distance-time graph from t = 5 s to t = 8 s means the object is stationary for 3 s.
A pre-paper checklist for graphs of motion
- Re-derive the two readings from scratch: gradient = (change on the vertical axis) divided by (change on the horizontal axis); area gives distance only on a speed-time graph.
- Know the three area shapes cold: rectangle = base multiplied by height, triangle = one half multiplied by base multiplied by height, trapezium = one half multiplied by (a plus b) multiplied by height.
- The exam gives you the labelled graph and the values at each corner; you supply the gradient and the area, so nothing needs memorising beyond the shape formulae.
- Before any calculation, write beside the graph that gradient = speed or acceleration and area = distance, so the two are never swapped.
- Check average speed at the end with total distance divided by total time, never the average of the stage speeds.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Should I revise distance-time and speed-time graphs together or separately?
Revise them side by side, because the trap is confusing the two. Both put time on the horizontal axis, but the gradient means something different on each, and only the speed-time graph gives distance as an area.
Studying them together trains you to check first which graph you are actually looking at.
How much of this chapter is just memorising area formulae?
Less than students fear. You only need three shapes: rectangle, triangle and trapezium.
The real skill is splitting a multi-stage speed-time graph into those shapes correctly, then reading the base and heights off the graph. Get the splitting right and the formulae do the rest almost automatically.
What is the fastest reliable check on my final answer?
Check the units and the scale. Acceleration must come out in m/s squared, a distance in metres, an average speed in m/s.
Then ask if the size is sensible: an average speed should sit between the slowest and fastest speeds on the graph. If it does not, you have added areas or times wrongly.