Lesson 1 · Time
Meet the clock rune
t is the number of seconds since a spell was cast. Multiplying it by 140 moves the spell 140 arena units every second.
By the end of this chapter
- ◇ Read t as elapsed time after a cast.
- ◇ Connect a coefficient to constant speed.
- ◇ Predict a spell position from its equation.
Study
Lesson notes
A clock built into every spell
Every cast starts its own clock at t = 0. One second later t = 1, after two seconds t = 2, and so on. An expression turns that changing number into a position.
In x(t) = 140t, each extra second adds another 140 arena units. Equal time steps create equal distances, so the spell moves at a constant speed.
Why speed is a trade-off
A larger multiplier reaches distant targets sooner and gives rivals less time to react. Magicomancy rewards slower sustained motion with more damage, so maximum speed is not always the strongest choice.
Worked example
Where is a spell with x(t) = 120t after 2.5 seconds?
- 1.Replace t with 2.5.
- 2.Multiply 120 × 2.5.
- 3.The sideways equation is 0, so it has not curved.
The spell is 300 units forward and 0 units sideways.
Predict before casting
If 140t becomes 210t, what changes?
Experiment
Spell laboratory
Compare 90t and 180t. Watch the one-second markers spread apart while the path stays straight.
Live spell notation
- x(t)
- 140 * t
- y(t)
- 0
The view uses the same 1600 × 900 scale as the workshop. Markers show equal one-second intervals.
Reference
Words for the spellbook
- Variable
- A symbol whose value can change. Here, t changes as the spell ages.
- Coefficient
- A number multiplying a variable. In 140t, the coefficient 140 controls speed.
- Constant rate
- The same amount of change during every equal interval of time.
Mastery challenge
Prove it in the workshop
The prepared spell is too slow. Change its forward coefficient so it reaches the target before the ten-second test ends.
Prepared Cartesian spell
x(t) = 70 * t
y(t) = 0
First hint
Start by changing 70 in x(t). Keep y(t) at zero so the path remains straight.