Formula 1
This activity belongs to the GeoGebra book The Domain of the Time.
In this construction, which simulates a simple video game, the car's speed depends on the result of applying an acceleration that we can vary with a slider (this same slider can be used to brake, as it allows for negative values). The goal is to complete a lap of the circuit in the shortest time possible, without going off the track.
If, when the light turns green, we activate the "Practice lap" checkbox, the acceleration will be fixed at a constant value (0.06), putting the car in uniformly accelerated motion, completing each lap in less time (until it goes off the track).
- Note: In the construction, the car (or the track) is not to scale.
- Note: For better performance, it is recommended to download the applet.
SCRIPT FOR SLIDER anima
# Calculate the elapsed seconds dt; add one second if t1(1) < tt
SetValue(tt, t1(1))
SetValue(t1, First(GetTime(), 3))
SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000)
# Moves M thanks to the acceleration "a" (vt is a unit vector tangent to the track)
SetValue(v, (abs(v) + dt a) vt)
SetValue(Aux, ClosestPoint(circuit, M + dt v))
SetValue(M, If(abs(Aux - M) < 0.1, Aux, M + dt v + dt (Aux - M)))
# Registers M for the polyline trace and controls the end
SetValue(reg, Append(reg, M))
StartAnimation(anima, abs(Aux - M) < 0.2)
SetValue(crash, abs(Aux - M) ≥ 0.2)
Author of the activity and GeoGebra construction: Rafael Losada.