S=ut+1/2(at^2) make t subject of formula
asked by guest
You asked:
Solve the equation
S = u t + 1 2 a t 2 S = u t + \frac{1}{2 a {t}^{2}} S = u t + 2 a t 2 1 for the unknown
t t t .
MathBot Answer:
t = − S 2 3 u 2 − S 3 u 3 + − 4 S 6 u 6 + ( − 2 S 3 u 3 + 27 2 a u ) 2 2 + 27 4 a u 3 + S 3 u − − S 3 u 3 + − 4 S 6 u 6 + ( − 2 S 3 u 3 + 27 2 a u ) 2 2 + 27 4 a u 3 3 t = − S 2 3 u 2 ( − 1 2 − 3 i 2 ) − S 3 u 3 + − 4 S 6 u 6 + ( − 2 S 3 u 3 + 27 2 a u ) 2 2 + 27 4 a u 3 + S 3 u − ( − 1 2 − 3 i 2 ) − S 3 u 3 + − 4 S 6 u 6 + ( − 2 S 3 u 3 + 27 2 a u ) 2 2 + 27 4 a u 3 3 t = − S 2 3 u 2 ( − 1 2 + 3 i 2 ) − S 3 u 3 + − 4 S 6 u 6 + ( − 2 S 3 u 3 + 27 2 a u ) 2 2 + 27 4 a u 3 + S 3 u − ( − 1 2 + 3 i 2 ) − S 3 u 3 + − 4 S 6 u 6 + ( − 2 S 3 u 3 + 27 2 a u ) 2 2 + 27 4 a u 3 3 \begin{aligned}t &= - \frac{S^{2}}{3 u^{2} \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}} + \frac{S}{3 u} - \frac{\sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}}{3}\\t &= - \frac{S^{2}}{3 u^{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}} + \frac{S}{3 u} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}}{3}\\t &= - \frac{S^{2}}{3 u^{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}} + \frac{S}{3 u} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}}{3}\end{aligned} t t t = − 3 u 2 3 − u 3 S 3 + 2 − u 6 4 S 6 + ( − u 3 2 S 3 + 2 a u 27 ) 2 + 4 a u 27 S 2 + 3 u S − 3 3 − u 3 S 3 + 2 − u 6 4 S 6 + ( − u 3 2 S 3 + 2 a u 27 ) 2 + 4 a u 27 = − 3 u 2 ( − 2 1 − 2 3 i ) 3 − u 3 S 3 + 2 − u 6 4 S 6 + ( − u 3 2 S 3 + 2 a u 27 ) 2 + 4 a u 27 S 2 + 3 u S − 3 ( − 2 1 − 2 3 i ) 3 − u 3 S 3 + 2 − u 6 4 S 6 + ( − u 3 2 S 3 + 2 a u 27 ) 2 + 4 a u 27 = − 3 u 2 ( − 2 1 + 2 3 i ) 3 − u 3 S 3 + 2 − u 6 4 S 6 + ( − u 3 2 S 3 + 2 a u 27 ) 2 + 4 a u 27 S 2 + 3 u S − 3 ( − 2 1 + 2 3 i ) 3 − u 3 S 3 + 2 − u 6 4 S 6 + ( − u 3 2 S 3 + 2 a u 27 ) 2 + 4 a u 27 t ≠ 0 t \neq 0 t = 0
