reaction

time

Time

Dist

D/(T^2)

Pred

Vel

Acc

B2 = 0.165
B3 = 2.93
C3 = 20
B4 = 4.69
C4 = 40
B5 = 6.35
C5 = 60
B6 = 7.96
C6 = 80
B7 = 9.63
C7 = 100
C2 = 0
S: (B2, C2)
B: (B3, C3)
C: (B4, C4)
D: (B5, C5)
E: (B6, C6)
F: (B7, C7)
data: {S, B, C, D, E, F}
D2 = 2.93
D3 = 4.69
D4 = 6.35
D5 = 7.96
D6 = 9.63
RT: B2
E2: C3 / (B3 - RT)^(2)
E3: C4 / (B4 - RT)^(2)
E4: C5 / (B5 - RT)^(2)
E5: C6 / (B6 - RT)^(2)
E6: C7 / (B7 - RT)^(2)
list1: {(D2, E2), (D3, E3), (D4, E4), (D5, E5), (D6, E6)}
g = FitPoly(list1, 3)
bd = Expand(g(x) * (x - RT)^(2))
abcde = Coefficients(bd)
a = Element(abcde, 1)
b = Element(abcde, 2)
c = Element(abcde, 3)
d = Element(abcde, 4)
e = Element(abcde, 5)
bv = Expand(5 * a * x^(4) + 4 * b * x^(3) + 3 * c * x^(2) + 2 * d * x + e)
ba = Expand(20 * a * x^(3) + 12 * b * x^(2) + 6 * c * x + 2 * d)
F2: bd(B2)
F3: bd(B3)
F4: bd(B4)
F5: bd(B5)
F6: bd(B6)
F7: bd(B7)
G2: bv(B2)
G3: bv(B3)
G4: bv(B4)
G5: bv(B5)
G6: bv(B6)
G7: bv(B7)
H2: ba(B2)
H3: ba(B3)
H4: ba(B4)
H5: ba(B5)
H6: ba(B6)
H7: ba(B7)
T_0: RT
T_F: B7
W: (T_F, 0)
f = Segment(S, W)
T = Point(f)
V: (x(T), bv(x(T)))
h = Segment(T, V)
i = Tangent(V, bv)
A = Point(i)
A' = Mirror(A, V)
j = Segment(A, A')
m_1 = Slope(j)
k = Integral(bv, x(S), x(T))
V_m = Extremum(bv, B2, B7)
A_z: (x(V_m), 0)
l = Segment(A_z, V_m)
V_1, V_2 = TurningPoint(bv)
V_w: (B7, bv(B7))
m = Segment(W, V_w)
A_1, A_2 = Extremum(ba, B2, B7)
n = Segment(A_1, V_1)
p = Segment(A_2, V_2)
A_s: (x(S), ba(x(S)))
A_w: (x(W), ba(x(W)))
q = Segment(A_w, W)
r = Segment(S, A_s)
s = Segment(W, F)