calc-013-derivada-concepto-velocidad

Uniforme/U. acelerado

t

t + Δt

Velocidad

espacio

tiempo

e(t)

e(t+Δt)

Δt = 3 (slider from 0 to 3)
n = false
f = If(n ≟ true, If[x ≥ 0, ((0.5 * 9.8) * x^(2))], If[x ≥ 0, (20 * x)])
A = Point(f)
h = Line(A, yAxis)
G = Intersect(h, xAxis)
D: (x(G) + Δt, y(G))
j = OrthogonalLine(D, xAxis)
B = Intersect(f, j)
c = Line(A, xAxis)
l = false
m = If(x(A) ≟ x(B), f'(x(A)), (y(B) - y(A)) / (x(B) - x(A)))
g: y - y(A) = (m * (x - x(A)))
a = Segment(A, B)
k = OrthogonalLine(A, yAxis)
C = Intersect(k, j)
i = Segment(A, C)
p = Segment(B, C)
E: (0, y(A))
F: (0, y(B))
delta = If(Δt ≟ 0, false, true)
texto1: "v(t)= \lim_{ Δt \to 0 } \frac{e(t+Δt) - e(t)}{Δt} =\\=" + (LaTeX[m]) + " m/s
              "
texto4: "v_m(t) = \frac{e(t+Δt) - e(t)}{Δt} =\\= " + (LaTeX[m]) + " m/s"