Vitesse instantanée
Author: M. Dewi Freitag

Vitesse instantanée

Vitesse moyenne

temps t (s)

position x (m)

f = Function((0.5 * ((0.5 * (x + 0.141)^(2)) - (0.042 * (x + 0.141)^(3)) + (0.001 * (x + 0.141)^(4)))) + 0.004, 0, 1000)
A = Point(f)
a = Tangent(A, f)
c = Circle(A, 3)
B, C = Intersect(c, a)
b = Segment(B, C)
d = OrthogonalLine(C, xAxis)
e = OrthogonalLine(B, yAxis)
D = Intersect(d, e)
g = Segment(B, D)
h = Segment(C, D)
pente = Slope(b)
text1: "pente = " + (Slope[b]) + " m/s"
i = OrthogonalLine(A, xAxis)
j = OrthogonalLine(A, yAxis)
E = Intersect(yAxis, j)
F = Intersect(i, xAxis)
k = Segment(A, F)
l = Segment(E, A)
text2: "t = " + (x(A)) + " s"
m = false
dt = 4 (slider from 0 to 8, step 0.1)
Fplus: (x(F) + dt, 0)
Fmoins: (x(F) - dt, 0)
n = OrthogonalLine(Fmoins, xAxis)
p = OrthogonalLine(Fplus, xAxis)
G = Intersect(f, p)
H = Intersect(f, n)
q = Segment(H, Fmoins)
r = Segment(Fplus, G)
s = Segment(Fmoins, Fplus)
t = Segment(H, G)
a_1 = OrthogonalLine(H, r)
I = Intersect(a_1, r)
b_1 = Segment(H, I)
o = false
c_1 = Line(H, G)
J = Intersect(d, c_1)
d_1 = OrthogonalLine(B, xAxis)
K = Intersect(c_1, d_1)
e_1 = Line(H, G)
text3: "x = " + (y(A)) + " m"
text5: "\Delta t = " + (LaTeX[(2 * dt)]) + " \,s"
L = Midpoint(b_1)
f_1 = Segment(I, G)
g_1 = Segment(I, Fplus)
M = Midpoint(f_1)
text4: "\Delta x = " + (LaTeX[Length[f_1]]) + "\,m\\v_m = \Delta x/\Delta t = " + (LaTeX[Slope[t]]) + "\,m/s"
N = Point(xAxis)
O = Point(yAxis)