Grade 11 Physics · SPH3U · nothing is recorded
The equations are hiding in the area.
Drag the two velocity handles (or focus one and use ↑ ↓). The area under the line splits into a rectangle and a triangle — and every displacement formula is just that picture, rearranged.
Velocity–time (uniform acceleration, Δt = 8 s)
speeding up [E] · a = 0.5 m/s²
Three ways, one answer
- rectangle (v₁ · Δt)
- 16 m
- triangle (½ (v₂−v₁) Δt)
- 16 m
- area = displacement
- 32 m
- v_av = (v₁+v₂)/2, then × Δt
- 4 m/s → 32 m
- Δd = v₁Δt + ½aΔt²
- 32 m
All three agree — they are the same picture, rearranged.
Predict, then look
A cart speeds up from 2 m/s [E] to 6 m/s [E] over 8 s. Predict its displacement.