Teacher copy · Velocity Arena
There is no single set of right numbers. Every bot has a different speed, so every team's answers are different — and different is correct. This key gives you one fully worked bot on the left and, for each step, the rule that tells you whether any team's answer is right on the right. Grade against the rule, not the numbers.
1-second distance = 31 cm.
First speed guess = 31 cm/sec.
Speed guess = their 1-second distance. Same number in both blanks. That is all this step is.
Range check: a bot's cm/sec is roughly its Speed stat × 7 or 8. A Speed-5 bot lands near 35–40; a Speed-10 bot near 70–80.
2 s: predict 31×2 = 62, actual 69, gap 62−69 = −7.
3 s: predict 31×3 = 93, actual 107, gap 93−107 = −14.
Bot went further than predicted, both times.
Prediction = their speed guess × time. Must be filled in before the actual — that is the whole point.
Both gaps should be negative (predicted < actual), and the 3-second gap should be bigger than the 2-second gap. If a team's gaps are near zero, their bot barely accelerates — fine, and rare.
Gap = predicted − actual, so "further than predicted" makes it negative. Do not correct a team that circled "further."
Three dots at (1, 31), (2, 69), (3, 107). They lie on a straight line.
a. Yes — a ruler touches all three.
b. Carried back to 0 seconds, the line hits below 0.
a. The three dots should be close to a straight line. Say yes unless one dot is wildly off (a measuring slip — have them redo it).
b. The right answer is below 0. Accept "below" or "a bit under zero." A team that says "at 0" hasn't extended the line far enough — point back at the graph, do not tell them.
107 − 69 = 38 cm.
"What does it represent?" → how far the bot goes in one extra second — its real speed.
Improved speed estimate = 38 cm/sec, bigger than the first guess of 31.
Answer = their 3-second distance − their 2-second distance.
It should come out bigger than their Step-1 guess, because the 1-second run was dragged down by start-up. If it comes out smaller, they subtracted the wrong way round.
This equals cm-per-second only because the runs are 1 second apart. A team that used 2 s and 4 s must divide their difference by 2.
A · full speed: 38×2 = 76 cm.
B · measured: 69 cm.
Start-up cost = B − A = 69 − 76 = −7 cm.
Must be B − A (measured − full speed), and must be negative. This is the most common error: a team that writes A − B gets a positive number and their whole equation ends up wrong.
Fast check: the start-up cost should be close to their 2-second gap from Step 2. For the worked bot both are −7. If those two numbers disagree, something upstream is off.
distance = 38 × time − 7
y = distance, x = time, m = 38, b = −7.
First blank = their improved speed (Step 5). Second blank = their start-up cost (Step 6), with its minus sign.
Because the sheet prints + before the second blank, a correct equation reads + −7, i.e. minus 7. Accept either + (−7) or a rewritten − 7.
4 s: predict 38×4 − 7 = 145, actual 145, gap 0.
5 s (never driven): predict 38×5 − 7 = 183 cm, then measured.
Prediction = their m × time + their b. The gap should now be small — a few cm — and much smaller than the Step-3 gap. That shrink is the point of the whole lab.
A zero gap is luck, not the bar. 2–3 cm is a success. If the gap is still large and negative, they likely kept the old speed or dropped the minus sign — walk back through Steps 5–7.
| Drive time (s) | Predicted (cm) | Actual (cm) | Gap | Change from run before |
|---|---|---|---|---|
| 1.0 | — | 31 | — | — |
| 2.0 | 62 | 69 | −7 | 38 |
| 3.0 | 93 | 107 | −14 | 38 |
| 4.0 | 145 | 145 | 0 | 38 |
| 5.0 | 183 | 183 | 0 | 38 |
m. Strong answers also note different start-up costs. This is the Model Swap idea arriving early; there is no single right sentence.