Finding gravity through experimental data

[BayernBlues]

Homework Statement

Experimentally measured time of fall
vs. distance for a freely falling object
Distance, x (m) Time, t (s)
0.1 0.148
0.2 0.196
0.3 0.244
0.4 0.290
0.5 0.315
0.6 0.352
0.7 0.385
0.8 0.403
0.9 0.429
1.0 0.451
Let the mathematical model be: x = 0.5gt^2 and assume that x = 0 at t = 0 :
a. In the light of what you learned in problem 1.1 (parts a and b) and the form of the equation
x = 0.5gt^2 , discuss (without calculations) two different methods that can be used to find g, the
acceleration due to gravity, from a straight line graph representation. In each method, indicate
explicitly the vertical variable, horizontal variable, slope, and intercept. Draw sketches.
b. Find a numerical estimate for g based on the above table, using the EXCEL program?

Homework Equations

x = 0.5gt^2

The Attempt at a Solution

I know that the value of g is 9.81 m/s^2 but this is asking how to show it through experimental data and graph. I think maybe taking the ln of both sides to change this into y=mx+b form might help but am unsure. Also, I thing g would be the constant in the equation if it was changed to y = mx + b form therefore it'd be the slope value.

 

[Gib Z]

It gives you the values of x and t, you have the equation that relates them. Solve for g.