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| -rw-r--r-- | assets/manual/manual.tex | 14 |
1 files changed, 5 insertions, 9 deletions
diff --git a/assets/manual/manual.tex b/assets/manual/manual.tex index fb36b93..0156169 100644 --- a/assets/manual/manual.tex +++ b/assets/manual/manual.tex @@ -1437,19 +1437,15 @@ This section is mainly intended as a reference that is provided for convenience. \subsection{Movement} -This section will use $x$ as the position and \( s = \Delta x \) as the distance. - \begin{align*} - v(T) &= v_0 + \int_0^T a(t) dt \\ - x(T) &= x_0 + \int_0^T v(t) dt \\ - s(T) &= \Delta x = \int_0^T v(t) dt + v &= \int a\, dt \\ + x &= \int v\, dt \\ \end{align*} \subsubsection{Constant acceleration} \begin{align*} - v(T) &= v_0 + \int_0^T a(t)dt = v_0 + aT \\ - x(T) &= x_0 + \int_0^T v(t)dt = x_0 + v_0T + \frac{1}{2}aT^2 \\ - s(T) &= v_0T + \frac{1}{2}aT^2 + 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: @@ -1461,7 +1457,7 @@ In certain cases, the starting velocity $v_0$ and the target velocity $v_1$ are \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 not that slopes are not taken into consideration. +Please note that slopes are not taken into consideration. \subsubsection{Acceleration constants} \begin{tabular}{|c|r|r|} |