Graphs of Motion · Form 4
Graphs of Motion: Common Mistakes
The mistakes that quietly cost marks in Graphs of Motion, and how to avoid each one in the SPM exam.
In our experience teaching Graphs of Motion, most lost marks come from a small set of repeated slips, not from a lack of understanding. Here they are, with the fix for each.
Mistakes to avoid
- Confusing a distance–time graph with a speed–time graph
- Forgetting units when reading a gradient
- Missing a part of the area when the graph has several stages
Six more slips that cost marks in graphs of motion
- What students write: average speed = (0 + 20 + 20 + 0) divided by 4. Why it loses marks: average speed is not the average of the speeds shown on the graph. Correct working: average speed = total distance divided by total time.
- What students write: a stage rising from 12 m/s to 24 m/s over 4 s taken as one half multiplied by 4 multiplied by 24 = 48 m. Why it loses marks: the stage starts at 12 m/s, so it is a trapezium, not a triangle. Correct working: one half multiplied by (12 plus 24) multiplied by 4 = 72 m.
- What students write: a stage running from t = 6 s to t = 16 s given a base of 16 s. Why it loses marks: the base is the length of the stage, not the final clock reading. Correct working: base = 16 minus 6 = 10 s.
- What students write: 72 km/h used directly with a time measured in seconds. Why it loses marks: the units do not match, so the distance is out by a factor. Correct working: 72 km/h = 72000 divided by 3600 = 20 m/s before using the seconds.
- What students write: the gradient of a distance-time graph labelled acceleration. Why it loses marks: on a distance-time graph the gradient is speed, not acceleration. Correct working: call it speed; acceleration is the gradient of a speed-time graph.
- What students write: the acceleration in a slowing stage given as 3 m/s squared. Why it loses marks: the object is slowing, so the acceleration is negative. Correct working: (12 minus 24) divided by 4 = negative 3 m/s squared, a deceleration of 3 m/s squared.
A 30-second self-check before you hand the paper in
- Read the axis label again: is the vertical axis speed or distance? That one word decides whether the gradient is acceleration or speed.
- For each area, glance at the two ends of the stage: if both are above zero the shape is a trapezium, not a triangle.
- Scan every base: each one should be an end time minus a start time, never a raw clock reading.
- Check every unit is written in: m/s squared for acceleration, m for distance, m/s for speed and average speed.
- Confirm any slowing stage carries a negative sign on its acceleration, and that your average speed used total distance over total time.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
I always forget whether a slowing stage is a triangle or a trapezium. How do I decide?
Look at the speed at the start and end of that stage. If either end is above zero, both vertical sides have length, so the shape is a trapezium.
It is only a triangle when the stage begins or ends exactly at 0 m/s, giving one side of zero height. Read the two heights off the graph before choosing.
The examiner marked my acceleration wrong even though the number was right. Why?
Usually the sign or the units. In a slowing stage the acceleration must be written as a negative value, and every acceleration answer needs the unit m/s squared.
A bare positive number for a deceleration, or a value with no unit, is treated as an incomplete answer even when the digits match.
Is it ever correct to just average the speeds shown on the graph?
Almost never for average speed. Averaging the corner speeds only happens to match when every stage lasts the same time, which is rare.
The safe rule is always total distance divided by total time. Treat any question that tempts you to average the speeds as a deliberate trap.