document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99620>Question 99620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve for t (time ) in the following equation. This is from a college physics book\r<BR>\n" );
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document.write( "y = initial velocity x time + 1/2 (acceleration) time ^2\r<BR>\n" );
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document.write( "-1.69 m = (1094 m/s )t + 1/2 ( -9.8 m/s^2 ) t ^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72479 by </B><A HREF=/tutors/aboutme.mpl?userid=Adam><B>Adam(64)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Adam><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=72479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is is a standard quadratic eaquation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and can be solved with formula with coefficients: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > I'll use my favourite notation :-),let's denote s for distance, t - time,a - acceleration,v0-initial velocity. then we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%281%2F2%29at%5E2%2Bv0t ALIGN=MIDDLE  ALT=\"s+=+%281%2F2%29at%5E2%2Bv0t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29at%5E2%2Bv0t-s=0 ALIGN=MIDDLE  ALT=\"%281%2F2%29at%5E2%2Bv0t-s=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > substituting into formula we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-v0+%2B-+sqrt%28+v0%5E2-2%2Aa%2As+%29%29%2F%28a%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-v0+%2B-+sqrt%28+v0%5E2-2%2Aa%2As+%29%29%2F%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > with values we get - getting two answers - -0.0015 and  223.2669 we can forget the negative one because it is phsically imposibble (time can never be negative) - btw those numbers in your equation seem really suspicious to me negative distance....that's either new theory of spacetime or....<BR>\n" );
document.write( "anyway quick rememberance:\r<BR>\n" );
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document.write( "s...distance[m],distance you travelled<BR>\n" );
document.write( "v...velocity[m/s],change of s during infinitesimal change of t ds/dt to be precise<BR>\n" );
document.write( "a...acceleration[m/s^2],dv/dt\r<BR>\n" );
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document.write( "How to have something from nothing...<BR>\n" );
document.write( "now, what I want to show is not fully rigorous, but it is a lot of fun :-),<BR>\n" );
document.write( "let's start with a = a with help of our formulae we can state that v=S[t]dt (primitive function) thus v = a*t+c now after deep thought we may state that constant will probably be v0, so v = a*t+v0, followed by s= V[t]dt<BR>\n" );
document.write( "s = 1/2a*t^2+v0*t+s0 (thought), now you try to make similiar conclusions, starting with a = 0. Good luck :-D \r<BR>\n" );
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