eliminate 't'?

Question

ELIMINATE 'T' FROM THE FOLLOWING EQUATION

2
U=U+GT,S=UT+1/2GT

Answer 1

I gues the question wrong or has printing mistakes.... please confirm in the first equation is it U= U+ GT or.... that woud make GT= 0;

Next in the second equation is it 1 by twice GT or is it half GT.

Answer 2

I think you mean these equations:

V=U+GT ............. (1)
S=UT+1/2*GT² ..... (2)
From equation (1)
GT = V - U
So T = (V - U)/G
Substitute into equation (2)
S = U(V - U)/G + 1/2 *G[(V - U)/G]²
= U(V - U)/G + (V - U)²/(2G)
Multiply both sides by 2G
2GS = 2UV - 2U² + V² - 2UV + U²
ie V² = U² + 2GS

Answer 3

2S = 2UT + GT
U = U + GT

If U = U + GT, then GT = 0. Therefore:

2S = 2UT

S = UT

The equations are now identities: U=U+0, S=S+0

Now if you mean u^2=u+gt, then u^2+s=u+ut+1 1/2g

2u^2+2s=2u+2ut+gt
2(u^2+s-u)=2ut+gt
(2(u^2+s-u))/(2u+g)=t

Then u^2=u+(2g(u^2+s-u))/(2u+g) and
s=(2u(u^2+s-u))+(2g(u^2+s-u))/(2(2u+g))

Answer 4

s=t(u+1/2g)

t=s/(u+1/2g)

substituting this in first

u= u+g(s/(u+1/2g))

simplify this