\textrm{Rovnoměrně zrychlený přímočarý pohyb - \textbf{parabola}}

v=a\cdot t\ \Rightarrow\ a=\frac{v}{t}\
s=\frac{1}{2}a\cdot t^2

\textrm{Zdůvodnění:}\
\vspace{1.5cm}
v(t)=\frac{ds}{dt}\ \Rightarrow\ s\!=\!\int\! v(t)\cdot dt\
s\!=\!\int \!a\cdot t\cdot dt=a\cdot\frac{t^2}{2}=\frac{1}{2}\cdot a\cdot t^2

\textrm{Př. Auto se rozjede z 0 na 100\frac{km}{h}\,za 40\,s.}\
\hspace{1cm}\textrm{Zobrazte graf ujeté dráhy v závislosti na čase.}

v=\textrm{100\frac{km}{h}=\frac{100\,000\,m}{3\,600\,s}=\frac{1\,000\,m}{36\,s}}\
\vspace{1.5cm}
a=\frac{v}{t}=\textrm{\frac{1000}{36\cdot40}m\cdot \!s^{-2}=\frac{25}{36}m\cdot \!s^{-2}}\
\vspace{1.5cm}
s=\frac{1}{2}\cdot a\cdot t^2=\frac{1}{2}\cdot\frac{25}{36}\cdot t^2=\frac{1}{2}\cdot \left( \frac{5}{6}\cdot t\right)^2\textrm[m]

t

y

\textrm\frac{6}{5}

\frac{1}{2}

\frac{12}{5}

2

\frac{18}{5}

\frac{9}{2}

\frac{24}{5}

8

y=s(t)

O = Intersect(xAxis, yAxis)
A: (6 / 5, 0.5)
B: (12 / 5, 2)
C: (18 / 5, 9 / 2)
D: (24 / 5, 8)
c = Conic(O, A, B, C, D)
E: (5, 0)
a = OrthogonalLine(A, xAxis)
b = OrthogonalLine(A, yAxis)
d = OrthogonalLine(B, xAxis)
e = OrthogonalLine(B, yAxis)
f = OrthogonalLine(C, xAxis)
g = OrthogonalLine(C, yAxis)
h = OrthogonalLine(D, xAxis)
i = OrthogonalLine(D, yAxis)
j = Segment(O, E)
P_1 = Point(j)
X_1 = Point(xAxis)
X_2 = Point(xAxis)
Y_1 = Point(yAxis)
Y_2 = Point(yAxis)
u = Vector(X_1, X_2)
v = Vector(Y_1, Y_2)
l = Segment(X_1, X_2)
m = Segment(Y_1, Y_2)
A_2 = Intersect(b, m)
B_2 = Intersect(e, m)
C_2 = Intersect(g, m)
D_2 = Intersect(i, m)
A_1 = Intersect(l, a)
B_1 = Intersect(l, d)
C_1 = Intersect(f, l)
D_1 = Intersect(h, l)
n = Segment(A, A_1)
p = Segment(B, B_1)
q = Segment(C, C_1)
r = Segment(D, D_1)
s = Segment(A, A_2)
t = Segment(B, B_2)
a_1 = Segment(C, C_2)
b_1 = Segment(D, D_2)
c_1 = OrthogonalLine(P_1, u)
P_2 = Intersect(c, c_1)
množina1 = Locus(P_2, P_1)