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Schreibt eure Formeln hier im Board am besten mit Latex!
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[quote="krid"]das Ausgangsintegral war: [Latex]\int \! \frac{v}{2-0,49v} \, \dd v [/Latex] durch Substitution: [Latex]u=2-0,49v[/Latex] [Latex]u'=-0,49[/Latex] [Latex]v = \frac{u-2}{-0,49}[/Latex] ergibt sich: [Latex]\int\frac{\frac{u-2}{-,049} }{u}*\frac{1}{-0,49} \, \dd u [/Latex] [Latex]\frac{1}{-0,49}* \int\frac{u-2}{-0,49*u} \, \dd u [/Latex] [Latex]\frac{1}{-0,49}* \int\frac{u}{-0,49*u} \, \dd u + \frac{1}{-0,49}* \int\frac{-2}{-0,49*u} \, \dd u[/Latex] [Latex]\frac{1}{(-0,49)^2}* \int 1 \dd u + \frac{-2}{(-0,49)^2}* \int\frac{1}{u} \, \dd u[/Latex] integriert: [Latex]\frac{1}{(-0,49)^2}*u + \frac{-2}{(-0,49)^2}*ln|u| [/Latex] rucksubstituiert: [Latex]\frac{1}{(-0,49)^2}*(2-0,49v) + \frac{-2}{(-0,49)^2}*ln|2-0,49v| [/Latex] in den Grenzen [Latex]v_0=3,33[/Latex] und [Latex]v=4,08[/Latex] ergibt t = 49,5 s eine lange Zeit, um von 3,33 m/s auf 4,08 m/s zu kommen ?([/quote]
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<table border="0" cellpadding="3" cellspacing="1" width="100%" class="forumline"> <tr> <th class="thCornerL" width="22%" height="26">Autor</th> <th class="thCornerR">Nachricht</th> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 12. Feb 2016 19:34<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">das Ausgangsintegral war: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int \! \frac{v}{2-0,49v} \, \dd v "> <br /> <br />durch Substitution: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?u=2-0,49v"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?u'=-0,49"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?v = \frac{u-2}{-0,49}"> <br /> <br />ergibt sich: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int\frac{\frac{u-2}{-,049} }{u}*\frac{1}{-0,49} \, \dd u "> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{1}{-0,49}* \int\frac{u-2}{-0,49*u} \, \dd u "> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{1}{-0,49}* \int\frac{u}{-0,49*u} \, \dd u + \frac{1}{-0,49}* \int\frac{-2}{-0,49*u} \, \dd u"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{1}{(-0,49)^2}* \int 1 \dd u + \frac{-2}{(-0,49)^2}* \int\frac{1}{u} \, \dd u"> <br /> <br />integriert: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{1}{(-0,49)^2}*u + \frac{-2}{(-0,49)^2}*ln|u| "> <br /> <br />rucksubstituiert: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{1}{(-0,49)^2}*(2-0,49v) + \frac{-2}{(-0,49)^2}*ln|2-0,49v| "> <br /> <br />in den Grenzen <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?v_0=3,33"> und <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?v=4,08"> <br /> <br />ergibt t = 49,5 s <br /> <br />eine lange Zeit, um von 3,33 m/s auf 4,08 m/s zu kommen <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 12. Feb 2016 12:19<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">vielen Dank <br />bekomme bei der Formel: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int \! \frac{x}{p-qx} \, \dd x = - \frac{p\cdot log(q\cdot x-p)+q\cdot x}{q^2} "> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int \! \frac{v}{2-0,49v} \, \dd v = - \frac{2\cdot log(0,49\cdot v-2)+0,49\cdot v}{0,49^2} "> <br /> <br /> und meinen Grenzen: <br /> <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?v_0 = 3,33"> <br /> <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?v = 4,08"> <br /> <br />mit dem Taschenrechner kein Ergebnis ( math. Fehler ) <br />setze ich aber bei dem Logarithmus das Ergebnis der Klammern absolut, <br />bekomme ich rund 20 raus. <br />Darf ich das und habe ich dann mein Ergebnis?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 11. Feb 2016 18:24<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">dann ... <br /> <br />... <a href="http://integrals.wolfram.com/index.jsp?expr=x%2F%28p-qx%29&random=false" target="_blank">http://integrals.wolfram.com/index.jsp?expr=x%2F%28p-qx%29&random=false</a></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 11. Feb 2016 16:03<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">das kann ich integrieren? <br /> <br /> <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /> <br /> <br />habe das abi vor 29 Jahren abgeschlossen</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 11. Feb 2016 00:15<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">v^2 / z sollte passen, aber v(z) ist eine Funktion von z, d.h. du darfst v^2 <span style="font-weight: bold">nicht</span> vor das Integral ziehen <br /> <br />es ist einfacher: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{1}{\frac{p}{v} - q} = \frac{v}{p - qv}"> <br /> <br />und das kannst du integrieren (oder nachschlagen)</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 11. Feb 2016 00:02<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">jetzt aber Schluss, bis morgen</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:59<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">irgendwo ist ein Fehler, denke ich</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:57<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">okay, dann hier noch der Rest: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? = \frac{v^2}{-2}\cdot \int\! \frac{1}{z} \, \dd z "> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? = \frac{v^2}{-2}\cdot ln | z |"> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? = \frac{v^2}{-2}\cdot ln |\frac{2}{v} - 0,49 |_{v_0}^v"> <br /> <br />und wenn ich die beiden Geschwindigkeiten einsetze, komme ich auf 58 Sekunden</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>franz</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:49<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Mit "Zitat" kommt man in den Quelltext von Beiträgen...</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:35<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">was habe ich falsch gemacht?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:34<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">okay, morgen geht's weiter <br />danke für eure Hilfe <br />viel spaß</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>franz</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:30<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>krid hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote">habe <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?t_{o}=0"> gesetzt und erhalte: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?t = \int_{v_0}^v \! \frac{1}{\frac{2}{v} -0,49} \, \dd v"> <br />Habe dann versucht :-) , durch Substitution zu Integrieren: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?z = \frac{2}{v} -0,49"> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?z' = \frac{2}{v} = \frac{-2}{v^2} "> <br />daraus folgt durch umstellen nach dv: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?dv = \frac{v^2}{-2} dz"> <br />also ist <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int \! \frac{1}{\frac{2}{v} -0,49} \, \dd v = \int \! \frac{1}{z}\cdot \frac{v^2}{-2} \, \dd z "></td> </tr></table><span class="postbody"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:28<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">warum hat es jetzt keine Formel geschrieben?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:22<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">habe [Latex]t_{o}=0[/Latex] gesetzt und erhalte: <br />[Latex]t = \int_{v_0}^v \! \frac{1}{\frac{2}{v} -0,49} \, \dd v[/Latex] <br />Habe dann versucht :-) , durch Substitution zu Integrieren: <br />[Latex]z = \frac{2}{v} -0,49[/Latex] <br />[Latex]z' = \frac{2}{v} = \frac{-2}{v^2} [/Latex] <br />daraus folgt durch umstellen nach dv: <br />[Latex]dv = \frac{v^2}{-2} dz[/Latex] <br />also ist <br />[Latex]\int \! \frac{1}{\frac{2}{v} -0,49} \, \dd v = \int \! \frac{1}{z}\cdot \frac{v^2}{-2} \, \dd z [/Latex]</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>franz</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:17<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Und rechne mal <span style="font-style: italic">ohne</span> Zwischenrundung.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 23:15<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?a(v) = \frac{p}{v} - q"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{dv}{dt} = \frac{p}{v} - q"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?dt = \frac{dv}{\frac{p}{v} - q}"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?t - t_0 = \int_{v_0}^v\frac{dv}{\frac{p}{v} - q}"> <br /> <br />Soweit passt das bei dir</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 22:58<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">sorry die Formel ist falsch: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int_{t_0}^t \! \, \dd t"> = <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int_{v_0}^v \! \frac{1}{\frac{2}{v} -0,49} \, \dd v"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 22:51<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int_{t_0}^t \! \, \dd t">= <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\int_{v_0}^v \! \frac{2}{v}-0,49 \, \dd v"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>krid</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 10. Feb 2016 22:14<span class="gen"> </span> Titel: Geschwindigkeitsabhängige Beschleunigung</span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><span style="font-weight: bold">Meine Frage:</span> <br />Ich habe eine Beschleunigung, die von der Geschwindigkeit abhängig ist. <br />a(v)= 2/v -0,49 <br />Die Beschleunigung nimmt mit zunehmender Geschwindigkeit ab. <br />Ich möchte wissen, wie lange die Beschleunigung anhält und die Beschleunigungsstrecke errechnen. <br />Die Anfangsgeschwindigkeit ist 12 km/h. <br /> <br /><span style="font-weight: bold">Meine Ideen:</span> <br />a = a(v) <br />a(v)= dv/dt <br />dt = dv/a(v) <br />komme mit dem Formeleditor nicht zurecht ;-) <br />bilde das Integral <br />und komme bei V0=3,33m/s und V1=4,08m/s <br />auf <br />-4,08²/2*ln|2/4,08-0,49|+3,33²/2*ln|2/3,33-0,49| <br />und somit auf rund 58 Sekunden. <br />Ziemlich viel :-)</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> </table>
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