blob: 5df11f9a56101bca5580cb5eff4c636b7b9c000a (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
|
\appendix
\part*{Appendices}
\addcontentsline{toc}{part}{Appendices}
\section{Physics}\label{s:physics}
This section is mainly intended as a reference that is provided for convenience.
\subsection{Movement}
\begin{align*}
v &= \int a\, dt \\
x &= \int v\, dt \\
\end{align*}
\subsubsection{Constant acceleration}
\begin{align*}
v &= v_0 + at \\
x &= x_0 + v_0t + \frac{1}{2}at^2
\end{align*}
In certain cases, the starting velocity $v_0$ and the target velocity $v_1$ are known:
\begin{align*}
t &= \frac{v_1 - v_0}{a} \\
s &= \frac{v_1^2 - v_0^2}{2a}
\end{align*}
\subsubsection{Acceleration of a train}
The acceleration of a train is calculate as follows:
\[a = a_{\text{all}} + a_{\text{locomotive}}\cdot\frac{n_{\text{locomotives}}}{n_{\text{wagons}}}\]
Please note that slopes are not taken into consideration.
\subsubsection{Acceleration constants}
\begin{tabular}{|c|r|r|}
\hline
Lever & $a_{\text{all}}$ & $a_{\text{locomotive}}$ \\
\hline
$0$ & $-10$ & $0$ \\
$1$ & $-3$ & $0$ \\
$2$ & $-0.5$ & $0$ \\
$3$ & $0$ & $0$ \\
$4$ & $0.5$ & $1.5$ \\
\hline
\end{tabular}
%%% Local Variables:
%%% TeX-master: "a4manual"
%%% End:
|
