Did you know? Areas below the time axis subtract from displacement but still contribute positively to distance travelled. G3 Physics tuition can help your child read a velocity-time graph by deciding which quantity the question asks for before adding the areas.
For an original example, a moving object travels at +3 m/s for 4 seconds, then at −2 m/s for 3 seconds. Its displacement is 12 − 6 = +6 m, while its distance travelled is 12 + 6 = 18 m. The negative sign describes direction, not a negative amount of travel.
The 2027 SEC G3 Physics syllabus is K323. It includes one-dimensional velocity-time graphs and determining displacement from their areas. Punggol parents can start by asking the child to label direction, area and units on the graph, then explain why distance and displacement may differ.
Find your next learning step
Match graph practice to K323 · Diagnose the quantity before the arithmetic · Calculate signed and total areas · Handle a graph that crosses zero · Check an unfamiliar graph without prompts
Match graph practice to K323
K323 includes speed, velocity, acceleration and graphical analysis of motion. The syllabus explicitly connects area under a velocity-time graph with displacement for uniform velocity or uniform acceleration.
This guide uses an idealised piecewise-constant motion example to isolate signed area. A real object changes velocity over a finite interval; a supplied graph determines whether that transition contributes additional area.
Read the official 2027 K323 Physics syllabus alongside the school’s current teaching programme.
Diagnose the quantity before the arithmetic
Ask what the vertical axis measures. A speed-time graph has non-negative speeds, whereas a velocity-time graph can show positive and negative directions. The labels determine the interpretation.
Then ask what the question requests: change in position, total path length or acceleration. Displacement comes from signed area; distance from adding the magnitudes of the motion segments; acceleration comes from gradient.
If the child finds a gradient when distance is requested, practise identifying the quantity. If the method is right but a triangle area is wrong, repair the geometry rather than reteaching all of kinematics.
Calculate signed and total areas
The first rectangle has area 3 × 4 = 12 m. It represents motion in the positive direction. The second has signed area −2 × 3 = −6 m, representing motion in the negative direction.
Adding signed areas gives displacement +6 m. Adding their magnitudes gives distance 18 m. The object ends 6 m in the positive direction from its starting point after travelling 18 m.
The unit check is useful: (m/s) × s = m. Counting graph squares without using the axis scales can produce the wrong area even when the shape is identified correctly.
| Segment | Signed area | Distance contribution |
|---|---|---|
| +3 m/s for 4 s | +12 m | 12 m |
| −2 m/s for 3 s | −6 m | 6 m |
| Total | +6 m displacement | 18 m distance |
Handle a graph that crosses zero
Suppose velocity changes uniformly from +2 m/s to −2 m/s over 4 seconds. It crosses zero after 2 seconds. There is a positive triangle of area 2 m and a negative triangle of signed area −2 m.
The net displacement is zero, but the distance travelled is 4 m. Split the region at the zero crossing before adding magnitudes. A single signed calculation can cancel two real parts of the journey.
At the zero crossing the object is momentarily at rest. A negative velocity means movement in the chosen negative direction; it does not by itself mean that the object is slowing down.
Check an unfamiliar graph without prompts
Ask the student to mark the zero crossings, choose relevant regions and write what each area represents. A reliable explanation should distinguish direction from path length.
Use a second graph with minutes on the horizontal axis and m/s on the vertical axis. The student must convert time consistently before reporting a distance in metres.
Bring the graph, question and working to a consultation. Ask whether support will address quantities, scales, signed areas or geometric calculations. Confirm that progress will be checked with new graphs.
Choose a focused next step
Continue with the related G3 Physics investigation guide and the Primary, PSLE and SEC subject directory.
For parents in Punggol, bring the actual subject level, examination year, recent work and teacher feedback. Ask what the proposed support will address and how independent progress will be checked. Confirm the provider’s subject availability before booking.
The Clementi Secondary 1 Mathematics guide illustrates diagnosis and focused 3-pax support. Looking closely at the student’s reasoning is a useful principle when choosing support for the actual subject and level.
Official syllabus checked 11 October 2026. The examples here are original teaching activities, not SEAB questions or official model answers.
