What you’ll explore
You ran a full lap. Your average velocity? Zero. In this lab you run a full lap back to the start and test your intuition against a real physics simulation.
Challenge levels
- One full lap. You run one full lap (400 m) at 5 m/s. What is your average velocity, in m/s?
- Half a lap. Now stop after half a lap (200 m) at 5 m/s. What is the size of your average velocity, in m/s?
- Just the bend. Run only the first bend (a half circle, radius 36.8 m) at 6 m/s. What is the size of your average velocity, in m/s?
- Half as fast. You run at 5 m/s. Choose where to stop so that your average velocity is exactly 2.5 m/s (±0.05).
- Get far away. Stop at the point on the track that is farthest from the start in a straight line. Get at least 128.5 m away.
Key ideas
Show the explanations (spoilers: try the levels first)
- You end where you started, so displacement is 0 m and average velocity is 0 m/s. Average speed is 400 m ÷ 80 s = 5 m/s.
- You end at the far corner, about 112 m from the start in a straight line. 112 m ÷ 40 s ≈ 2.80 m/s, while your speed was 5 m/s the whole time.
- Along the bend you cover πR ≈ 115.6 m, but the straight line across is 2R = 73.6 m. Average velocity = speed × 2/π ≈ 3.82 m/s.
- Average velocity = displacement ÷ time, and time = distance ÷ 5. You need to end up exactly half as far from the start as the distance you ran.
- The farthest point is on the far bend, on the line from the start through the bend’s centre: √(84.39² + 36.8²) + 36.8 ≈ 128.9 m.
About the model
- Track: lane-1 measurement line, bend radius 36.80 m; straights set to 200 − 36.8π ≈ 84.389 m so one lap is exactly 400 m (rulebook 84.39 m gives 400.0012 m).
- Runner is a point moving at constant speed along the line; start and stop are instant (no acceleration phase). Before the clock starts, velocity is 0.
- Displacement is measured in the track plane from the start line to the runner; average velocity = displacement ÷ run time.
- Arrows: velocity drawn 3 m per 1 m/s; the runner marker is enlarged for visibility (not to scale).
Every number on screen comes from the simulation, and each lab passes automated checks against the physics formulas. Spotted a mistake? Tell us.