✅ Adventure 6 — Activity 1 Solutions
Rectangle Table (Δt = 1)
| Interval | Δt | Velocity | vΔt |
|---|---|---|---|
| 0–1 | 1 | 0 | 0 |
| 1–2 | 1 | 7 | 7 |
| 2–3 | 1 | 12 | 12 |
| 3–4 | 1 | 15 | 15 |
| 4–5 | 1 | 16 | 16 |
| 5–6 | 1 | 15 | 15 |
| 6–7 | 1 | 12 | 12 |
| 7–8 | 1 | 7 | 7 |
| Total | 84 |
Comparison Table
| Width (Δt) | Method | Sum of Areas |
|---|---|---|
| 1 | Your Estimate | 84 |
| 1/2 | Finer estimate | 85.21 |
| 1/4 | Very fine estimate | 85.31 |
3) Integral Calculation
S = ∫₀⁸ (8t − t²) dt
= [4t² − (1/3)t³]₀⁸
= 256 − 512/3
= 85⅓ ≈ 85.33 m
