位移與時間的關係
Author: 藍邦偉  老師

$ O $

$第$%v$步$

$ t$

$f(t)為$%v$次函數$

$ s$

$ 位移與時間的關係 $

O = (0, 0)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
n = 0 (slider from 0 to 3, step 1)
A_1 = (3, 2)
A_2 = (2, 3)
A_3 = (6, 5)
A_4 = (9, 6)
k = 1 (slider from 1 to 3, step 1)
f_2 = Function(Polynomial[{A_1, A_2, A_3}], 0, 11)
m_1 = Slope(Line[A_1, A_2])
v = Vector((0, 0), (0, y(Corner[3])))
u = Vector((0, 0), (x(Corner[3]), 0))
t = 0.49 (slider from 0 to 10, step 0.01)
P_2: (t, f_2(t))
a_2 = Tangent(P_2, f_2)
f_3 = Function(Polynomial[{A_1, A_2, A_3, A_4}], 0, 12)
f_1 = Function(Polynomial[{A_1, A_2}], 0, 12)
g_2 = Derivative(f_2)
h_2 = Derivative(g_2)
P_3: (t, f_3(t))
a_3 = Tangent(P_3, f_3)
g_3 = Derivative(f_3)
h_3 = Derivative(g_3)
text1: "$ v(t) =s'(t)=\frac{ds}{dt}$
$\;\;\;\;\;\;\;=s'(" + (LaTeX[t]) + ")=" + (LaTeX[If[k ≟ 1, Slope[Line[A_1, A_2]], If[k ≟ 2, g_2(t), If[k ≟ 3, g_3(t)]]]]) + "$
$a(t)=s''(t)=\frac{d^2s}{dt^2}$
$\;\;\;\;\;\;\;=s''(" + (LaTeX[t]) + ")=" + (LaTeX[If[k ≟ 1, 0, If[k ≟ 2, h_2(t), If[k ≟ 3, h_3(t)]]]]) + "$"
t_1: "$ " + (LaTeX[If[m_1 > 0, "速度遞增", If[m_1 < 0, "速度遞減", "等速度運動"]]]) + " $
$等速運動，\;加速度為0$"
A = (-5, 5)
text2: "$ " + (LaTeX[If[g_2(t) > 0, "速度遞增", If[g_2(t) < 0, "速度遞減", "等速運動"]]]) + " $
$等加速度運動$"
text3: "$ " + (LaTeX[If[g_3(t) > 0, "速度遞增", If[g_3(t) < 0, "速度遞減", "等速運動"]]]) + " $
$" + (LaTeX[If[h_3(t) > 0, "加速度為正", If[h_3(t) < 0, "加速度為負", "等速運動"]]]) + "$"