$ Weg\,\,in\,\,Meter $

$ Zeit\,\,in\,\,Sekunden $

Radarfalle nach
71 Sekunden Fahrzeit !

$ Phase\,\,I $

x_1 = 54 (slider from 0 to 120, step 0.1)
f_1 = Function(2 / 5 * x, 0, 20)
F_1 = Function(Integral[f_1, x], 0, 20)
f_5 = Function(15 / 100 * (x - 85)^(2) + 5, 75, 85)
f_2 = Function(8, 20, 40)
f_4 = Function(4 / 5 * (x - 50), 50, 75)
f_3 = Function(2 / 25 * (x - 50)^(2), 40, 50)
f_6 = Function(5 / 14 * (x - 85) + 5, 85, 120)
I_1 = Integral(f_1, 0, 20)
I_2 = Integral(f_2, 20, 40)
I_3 = Integral(f_3, 40, 50)
I_4 = Integral(f_4, 50, 75)
I_5 = Integral(f_5, 75, 85)
I_6 = Integral(f_6, 85, 120)
Gesamtweg: I_1 + I_2 + I_3 + I_4 + I_5 + I_6
F_2 = Function(Integral[f_2, x] - Integral[f_2, 0, 20] + I_1, 20, 40)
F_3 = Function(Integral[f_3, x] - Integral[f_3, 0, 40] + I_1 + I_2, 40, 50)
F_4 = Function(Integral[f_4, x] - Integral[f_4, 0, 50] + I_1 + I_2 + I_3, 50, 75)
F_6 = Function(Integral[f_6, x] - Integral[f_6, 0, 85] + I_1 + I_2 + I_3 + I_4 + I_5, 85, 120)
F = Point(f_6)
Text2 = LaTeX(F, true, true)
O = Point(f_4)
Text3 = LaTeX(O, true, true)
Geschw = 18.1 (slider from 0 to 25, step 0.1)
P: (0, Geschw)
Q: (120, Geschw)
g = Segment(P, Q)
R: (y(P) * 3.6, 1000)
Text4: "vmax: " + (x(R)) + " km/h"
A = Intersect(I_4, f_4, 2)
B = Intersect(f_4, g, 2)
Text1 = LaTeX(B, true, true)
C = (71, 0)
Radarfalle: (71, F_4(71))
a = Segment(C, Radarfalle)
F_5 = Function(Integral[f_5, x] - Integral[f_5, 0, 75] + I_1 + I_2 + I_3 + I_4, 75, 85)
D: (x_1, F_1(x_1))
E: (x_1, F_2(x_1))
G: (x_1, F_3(x_1))
H: (x_1, F_4(x_1))
I: (x_1, F_5(x_1))
J: (x_1, F_6(x_1))
P_1 = If((0 ≤ x_1) ∧ (x_1 ≤ 20), D, If[(20 < x_1) ∧ (x_1 ≤ 40), E, If[(40 < x_1) ∧ (x_1 ≤ 50), G, If[(50 < x_1) ∧ (x_1 ≤ 75), H, If[(75 < x_1) ∧ (x_1 ≤ 85), I, J]]]])
x_2 = 96 (slider from 0 to 120, step 0.1)
K: (x_2, F_1(x_2))
L: (x_2, F_2(x_2))
M: (x_2, F_3(x_2))
N: (x_2, F_4(x_2))
S: (x_2, F_5(x_2))
T: (x_2, F_6(x_2))
P_2 = If((0 ≤ x_2) ∧ (x_2 ≤ 20), K, If[(20 < x_2) ∧ (x_2 ≤ 40), L, If[(40 < x_2) ∧ (x_2 ≤ 50), M, If[(50 < x_2) ∧ (x_2 ≤ 75), N, If[(75 < x_2) ∧ (x_2 ≤ 85), S, T]]]])
U: (x(P_2), y(P_1))
Vieleck1, p_2, p_1, u = Polygon(P_1, U, P_2)
b = Segment(P_2, U)
c = Segment(P_1, U)
Text10: "$ \Delta\,t\,=\," + (LaTeX[c]) + "\,s $"
P2 = 0
P_3: (x(P_1) / 2 + x(P_2) / 2, y(P_1))
Text11: "$ \Delta\,S\,=\," + (LaTeX[p_1]) + "\,m $"
V: (x(U), y(P_2) / 2 + y(U) / 2)
Geschwindigkeit: ((y(P_2) - y(P_1)) / (x(P_2) - x(P_1)) * 3.6, 0)
Text6: "$ x_{2}=" + (LaTeX[x_2]) + "\,s $"
Text13: "$ x_{1}=" + (LaTeX[x_1]) + "\,s $"
Z: ((y(P_2) - y(P_1)) / (x(P_2) - x(P_1)), 0)
Text12: " v\,=\," + (LaTeX[x(Geschwindigkeit)]) + "\,\,\frac{km}{h} =" + (LaTeX[x(Z)]) + "\,\,\frac{m}{s}"