Question

solve for G. S=1/2gt^2

Answer 1

Is this for differential equations? Or do you have values for s and t?

Answer 2

differential equations

Answer 3

Just differentiate the equation twice with respect to t.
It's a pattern, if you differentiate S(displacement) once, you get velocity, and twice, you get acceleration which is equal to g (gravity).

So, 1st: ds/dt or V for velocity=1/2g(2t) = v=gt
2nd: dV/dt or a for acceleration = g(1), a=g.

I would usually say g=9.8066 m/s^2 coz that's the usual value for gravity in the Earth, but that'll be a different value if it's in another planet or the moon.