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Question Number 171773 by Mikenice last updated on 20/Jun/22

make T the subject of the formula if  s=ut+(1/2)at^2

$${make}\:{T}\:{the}\:{subject}\:{of}\:{the}\:{formula}\:{if} \\ $$$${s}={ut}+\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \\ $$

Answered by thfchristopher last updated on 21/Jun/22

T? Or t?  s=ut+(1/2)at^2   ⇒2s=2ut+at^2   ⇒at^2 +2ut−2s=0  ⇒t=((−2u±(√(4u^2 +8as)))/(2a))  =((−u±(√(u^2 +2as)))/a)

$${T}?\:\mathrm{O}{r}\:{t}? \\ $$$${s}={ut}+\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{2}{s}=\mathrm{2}{ut}+{at}^{\mathrm{2}} \\ $$$$\Rightarrow{at}^{\mathrm{2}} +\mathrm{2}{ut}−\mathrm{2}{s}=\mathrm{0} \\ $$$$\Rightarrow{t}=\frac{−\mathrm{2}{u}\pm\sqrt{\mathrm{4}{u}^{\mathrm{2}} +\mathrm{8}{as}}}{\mathrm{2}{a}} \\ $$$$=\frac{−{u}\pm\sqrt{{u}^{\mathrm{2}} +\mathrm{2}{as}}}{{a}} \\ $$

Answered by MikeH last updated on 21/Jun/22

at^2 +2ut−2s=0  quadratic equation  t = ((−2u±(√(4u^2 +4as)))/(2a))  ⇒ t = ((−u±(√(u^2 +as)))/a)

$${at}^{\mathrm{2}} +\mathrm{2}{ut}−\mathrm{2}{s}=\mathrm{0} \\ $$$$\mathrm{quadratic}\:\mathrm{equation} \\ $$$${t}\:=\:\frac{−\mathrm{2}{u}\pm\sqrt{\mathrm{4}{u}^{\mathrm{2}} +\mathrm{4}{as}}}{\mathrm{2}{a}} \\ $$$$\Rightarrow\:{t}\:=\:\frac{−{u}\pm\sqrt{{u}^{\mathrm{2}} +{as}}}{{a}} \\ $$

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