T

Σημείο t

Μέση Ταχύτητα

Συνάρτηση Μέσης Ταχύτητας

ε-ζώνη

δ-ζώνη

t

a = 0 (slider from -5 to 5, step 0.1)
b = 12 (slider from -5 to 12, step 0.1)
T = 6 (slider from 0 to 12, step 0.1)
c = 0 (slider from -2 to 2, step 0.01)
p = -0.131 (slider from -5 to 5, step 0.1)
r = -0.0020 (slider from -5 to 5, step 0.1)
q = 2.453 (slider from -5 to 5, step 0.1)
f = Function(p * x^(2) + q * x + r, a, T)
g = Function(p * x^(2) + q * x + r + c, T, b)
A: (T, f(T))
B: (T, 0)
C: (0, f(T))
d = Segment(A, B)
D: (a, f(a))
F: (a, 0)
G: (b, 0)
h = Segment(D, F)
ε = 0.88 (slider from 0 to 2, step 0.0010)
δ = 3.37 (slider from 0 to 4, step 0.0010)
H: (T - δ, 0)
I: (T + δ, 0)
j = OrthogonalLine(H, xAxis)
k = OrthogonalLine(I, xAxis)
J: (0, f(T) - ε)
K: (0, f(T) + ε)
l = OrthogonalLine(K, yAxis)
m = OrthogonalLine(J, yAxis)
L = Intersect(j, l)
M = Intersect(k, l)
N = Intersect(k, m)
O = Intersect(j, m)
πολύγ.1, o, l_1, m_1, n = Polygon(O, L, M, N)
toppoint = 100 (slider from 0 to 100, step 0.1)
P: (T - δ, y(L) + toppoint)
Q: (T - δ, y(O) - toppoint)
s = OrthogonalLine(P, j)
a_1 = OrthogonalLine(Q, j)
R = Intersect(k, s)
S = Intersect(k, a_1)
T_1: (T, g(T))
b_1 = Segment(B, T_1)
U: (0, g(T))
c_1 = Segment(T_1, U)
d_1 = Segment(L, O)
e_1 = Segment(M, N)
πολύγ.2, l_2, p_1, r_1, m_2 = Polygon(L, P, R, M)
πολύγ.3, o_1, n_1, s_1, q_1 = Polygon(O, N, S, Q)
intf(x) = p * x^(3) / 3 + q * x^(2) / 2 + r * x
κείμενο1: "s(T) = " + (intf(T)) + "m"
t = 2.04 (slider from 0 to 12, step 0.0010)
κείμενο2: "s(t) = " + (intf(t)) + "m"
pointt = false
meanv = false
meanfunction = false
ezone = false
dzone = false
V: (t, 0)
mv = Function((intf(T) - intf(x)) / (T - x), a, b)
W: (t, mv(t))
E: (0, mv(t))
i = Segment(E, W)
f_1 = Segment(W, V)
κείμενο3: "$\frac{s(T) - s(t)}{T-t}=" + (LaTeX[mv(t)]) + "$"

Tool: Ύψος Τριγώνου (command ύψος)
Διαλέξτε τις τρεις κορυφές. Πρώτα αυτήν από την οποία θα φέρουμε το ύψος.
Input: Α, Β, Γ
Output: E, m, α, l

e = Line(Β, Γ)
k = OrthogonalLine(Α, e)
E = Intersect(e, k)
l = Segment(E, Α)
m = Segment(E, Β)
α = Angle(Β, E, Α)