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| Line 102: | Line 102: | ||
===Time=== | ===Time=== | ||
As with acceleration, time to decelerate from maximum warp velocity is worked out by rearranging the velocity equation. | |||
<math>\pagecolor{Black}\color{White} | <math>\pagecolor{Black}\color{White} | ||
\begin{align} | \begin{align} | ||
v &= k*e^{jt}\\ | |||
= \frac{k | \frac{v}{k} & = e ^ {jt}\\ | ||
t & = \frac{\ln{(\frac{v}{k})}}{j} | |||
\end{align} | \end{align} | ||
</math> | |||
While the deceleration from ''s'' to 0 was insignificant in terms of distance, it is significant in terms of time. This means that the time to decelerate is calculated as follows: | |||
<math>\pagecolor{Black}\color{White} | |||
\begin{align} | |||
t_{decel} & = t_{decel\_warp} - t_{decel\_s}\\ | |||
& = \frac{\ln{(\frac{v}{k})}}{j} - \frac{\ln{(\frac{s}{k})}}{j}\\ | |||
& = \frac{\ln{(\frac{v}{k})} - \ln{(\frac{s}{k})}}{j}\\ | |||
& = \frac{\ln{v} - \ln{k} - ln{s} + ln{k}}{j}\\ | |||
& = \frac{\ln{v} - \ln{s}}{j}\\ | |||
& = \frac{\ln{(\frac{v}{s})}}{j}\\ | |||
</math> | </math> | ||