Problem: If V=gt+V0V=g t+V_{0}V=gt+V0 and S=1/2gt2+VotS=1 / 2 g t^{2}+V_{o} tS=1/2gt2+Vot then ttt equals
Answer Choices:
A. 2SV+V0\dfrac{2 S}{V+V_{0}}V+V02S
B. 2SV−V0\dfrac{2 S}{V-V_{0}}V−V02S
C. 2SV0−V\dfrac{2 S}{V_{0}-V}V0−V2S
D. 2SV\dfrac{2 S}{V}V2S
E. 2S−V2 S-V2S−V Solution:
2S=gt2+2V0t;Vt=gt2+V0t;∴2S−Vt=V0t;2 S=g t^{2}+2 V_{0} t ; \quad V t=g t^{2}+V_{0} t ; \quad \therefore 2 S-V t=V_{0} t; 2S=gt2+2V0t;Vt=gt2+V0t;∴2S−Vt=V0t;
∴t=2SV+V0\therefore t=\dfrac{2 S}{V+V_{0}} ∴t=V+V02S
or
g=V−V0t,S=12V−V0t⋅t2+V0t=t(12V+12V0).g=\dfrac{V-V_{0}}{t}, S=\dfrac{1}{2} \dfrac{V-V_{0}}{t} \cdot t^{2}+V_{0} t=t\left(\dfrac{1}{2} V+\dfrac{1}{2} V_{0}\right) . g=tV−V0,S=21tV−V0⋅t2+V0t=t(21V+21V0).
∴t=2SV+V0.\therefore t=\dfrac{2 S}{V+V_{0}} . ∴t=V+V02S.