Velocity Arena
Your job today: predict how far your bot will travel — before it moves. Then measure what really happens and work out why the two are different.
You need a tape measure and a start line. Line the back wheels up behind the start line every single time, or your numbers will not mean anything.
Set the drive time to 1.0 second and press A. Measure how far it went.
Put a dot for each run. You choose the numbers up the side — look at your biggest distance first, then pick a scale that fits it. You will come back and add more dots later.
a. Could you lay a ruler on all three dots and have them line up? YES NO
b. If you carried that line backwards to the left edge (0 seconds), would it hit exactly at 0, above 0, or below 0?
a. Trial 2 gap: cm Trial 3 gap: cm
b. Is the gap getting bigger or smaller as you drive longer?
c. Is your bot going further than you predicted, or less far?
d. Your speed number came from the 1 second run. What is your bot doing during that first second that it is not doing later on?
a. Which team did you talk to?
b. Is their gap growing too? YES NO
c. What do you both think is causing it?
Do this arithmetic first. Do not write down what it means yet.
What does that number represent? Your two runs were 2 seconds and 3 seconds. Say your answer out loud to your team first, then write it.
Your 2-second run and your 3-second run both started from a standstill, so both lost the same amount of distance getting up to speed.
When you subtract one from the other, that loss cancels out. What is left is one clean second of driving, with no starting up inside it.
Your bot spends part of the first second speeding up instead of moving at full speed. The distance it loses doing that becomes a negative starting value in your equation.
Now work out how big that lost distance is:
| distance — what we predict | y |
| time — what we choose | x |
| our speed, cm per second | m |
| our start-up cost | b |
Pick a drive time you have not tried yet. Predict it with your equation, write it down, then drive it. Getting this one right is the strongest proof your equation actually works.
Go back to your graph in Step 4 and add these last two dots. Do all five line up?
Copy your results into this table. Bring this sheet tomorrow — you will use the Drive time and Actual columns to build your team's equation.
| Drive time (seconds) |
Predicted (cm) |
Actual (cm) |
Gap (pred − actual) |
Change from the run before (cm) |
|---|---|---|---|---|
| 1.0 | — | — | — | |
| 2.0 | ||||
| 3.0 | ||||
| 4.0 | ||||
The shaded column is the only one you actually measured. Every other number on this sheet was worked out from it.
a. The last column is how much further your bot went for each extra second. Are those numbers close to each other?
b. If they are close, your measuring was good. If they jump around a lot, tell your teacher — check the batteries and your start line before trusting your equation.
c. Where else on this sheet did that number show up?
Write each gap as a plain positive number — how many cm off you were, whether too far or too short.
Our gap on Trial 2 was cm.
Our gap on our last trial was cm.
The change that helped most was
a. Another team's equation will not be the same as yours. Why not? Your bots ran the same code.
b. Write their two numbers next to yours:
Our speed their speed
Our start-up cost their start-up cost
c. Which one differed more between your two teams — the speed or the start-up cost?
d. Why do you think that one varies more?