motion

$Let\quad 'u'\quad be\quad the\quad initial\quad velocity\quad and\quad let\quad 'a'\quad be\quad the\quad constant\quad \\ acceleration\quad of\quad the\quad body.Distance\quad covered\quad in\quad { n }^{ th }\quad second\\ is\quad given\quad by\\ Distance\quad covered\quad in\quad n\quad seconds-Distance\quad covered\quad in\quad (n-1)\\ seconds:\\ \\ { s }_{ n }-{ s }_{ n-1 }\\ un+\frac { a }{ 2 } ({ n }^{ 2 })-[u(n-1)+\frac { a }{ 2 } { (n-1) }^{ 2 }]\\ un-un+u+\frac { a{ n }^{ 2 } }{ 2 } -\frac { a{ n }^{ 2 } }{ 2 } -\frac { a }{ 2 } +an\\ u+an-\frac { a }{ 2 } \\ u+\frac { a }{ 2 } [(2n-1)$

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