The ten-centimeter dash
Frame-by-frame photos of the beetle crossing the tile, one frame per second. Speed for each interval = distance traveled ÷ time elapsed. The first row is done for you. Fill in the shaded cells.
| Time (s) | Position (cm) | Distance this interval (cm) | Speed this interval (cm/s) |
|---|---|---|---|
| 0 → 1 | 0.0 → 1.6 | 1.6 | 1.6 |
| 1 → 2 | 1.6 → 3.4 | ||
| 2 → 3 | 3.4 → 4.8 | ||
| 3 → 4 | 4.8 → 5.0 | ||
| 4 → 5 | 5.0 → 5.2 |
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During which interval was the beetle moving fastest? How can you tell from the numbers alone — no photos?
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The beetle's two "cruise" intervals and its two "scurry… then stop" intervals tell a story. Write one sentence: what happened between second 3 and second 5?
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Average speed for the whole dash = total distance ÷ total time. Compute it. Why is the average slower than the fastest interval?
Who's faster?
Races with different distances can't be settled by times alone — you need unit rates (meters per 1 second). Show the rate for each runner, then crown a winner.
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Runner A covers 100 m in 20 s. Runner B covers 60 m in 10 s.
- Speed of A:
- Speed of B:
- Who is faster? Why does the shorter time NOT automatically win?
- Speed of A:
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A garden snail covers 30 cm in 2 minutes. The beetle covers 5.2 cm in 5 s. Convert both to cm per second and compare. (Careful — minutes vs seconds.)
The fastest human, in intervals
Simplified split data from a world-class 100 m sprint. Each "split" is the time to cover that 10 m chunk — not the clock time.
| Chunk | Split time (s) | Speed for this chunk (m/s) |
|---|---|---|
| 0 – 10 m | 1.9 | |
| 10 – 20 m | 1.0 | |
| 80 – 90 m | 0.9 |
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Compute the speed for each chunk (round to one decimal). Where in the race was the sprinter fastest — the start, the middle, or the end?
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Why is the first chunk the slowest even though the sprinter is trying hardest then? One sentence, using the word acceleration.
Draw the story
"I walked to my friend's house in 4 minutes, realized I forgot the snack, stood still for 2 minutes deciding what to do, then ran home in 1 minute." Sketch the distance-from-home–time graph on the grid. Label the three segments.
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Which segment is steepest? What does steepness mean on a distance–time graph?
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What does a flat (horizontal) segment mean? What does a segment that comes back down mean?
Answer key — teachers
Part A
Table: 1→2 s: 1.8 cm, 1.8 cm/s · 2→3 s: 1.4 cm, 1.4 cm/s · 3→4 s: 0.2 cm, 0.2 cm/s · 4→5 s: 0.2 cm, 0.2 cm/s.
- Interval 1→2 s (1.8 cm/s) — it covers the most distance in the same time.
- The beetle slowed almost to a stop — roughly crawling (0.2 cm/s ≈ stopped for a beetle; accept "it nearly stopped / was resting").
- 5.2 cm ÷ 5 s = 1.04 cm/s. The average blends the fast start with the slow finish.
Part B
- a) 100 ÷ 20 = 5 m/s · b) 60 ÷ 10 = 6 m/s · c) B is faster — B ran less far; only the rate (distance per 1 second) compares fairly.
- Snail: 30 cm ÷ 120 s = 0.25 cm/s. Beetle: 5.2 ÷ 5 = 1.04 cm/s. Beetle ≈ 4× faster.
Part C
- 5.3 m/s · 10.0 m/s · 11.1 m/s. Fastest at the end (80–90 m).
- From a standstill the sprinter must accelerate — speed builds over the race; you can't start at top speed.
Part D
- Correct graph: rising segment (4 min) → flat (2 min) → falling steep segment (1 min). The run home is steepest — steepness = speed.
- Flat = stopped (time passes, distance doesn't). Coming down = returning toward the start.