Question Number 171773 by Mikenice last updated on 20/Jun/22
$${make}\:{T}\:{the}\:{subject}\:{of}\:{the}\:{formula}\:{if} \\ $$$${s}={ut}+\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \\ $$
Answered by thfchristopher last updated on 21/Jun/22
$${T}?\:\mathrm{O}{r}\:{t}? \\ $$$${s}={ut}+\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{2}{s}=\mathrm{2}{ut}+{at}^{\mathrm{2}} \\ $$$$\Rightarrow{at}^{\mathrm{2}} +\mathrm{2}{ut}−\mathrm{2}{s}=\mathrm{0} \\ $$$$\Rightarrow{t}=\frac{−\mathrm{2}{u}\pm\sqrt{\mathrm{4}{u}^{\mathrm{2}} +\mathrm{8}{as}}}{\mathrm{2}{a}} \\ $$$$=\frac{−{u}\pm\sqrt{{u}^{\mathrm{2}} +\mathrm{2}{as}}}{{a}} \\ $$
Answered by MikeH last updated on 21/Jun/22
$${at}^{\mathrm{2}} +\mathrm{2}{ut}−\mathrm{2}{s}=\mathrm{0} \\ $$$$\mathrm{quadratic}\:\mathrm{equation} \\ $$$${t}\:=\:\frac{−\mathrm{2}{u}\pm\sqrt{\mathrm{4}{u}^{\mathrm{2}} +\mathrm{4}{as}}}{\mathrm{2}{a}} \\ $$$$\Rightarrow\:{t}\:=\:\frac{−{u}\pm\sqrt{{u}^{\mathrm{2}} +{as}}}{{a}} \\ $$