How can I mathematically find the acceleration of an object from the position graph of the object?

I don't want to draw the velocity and acceleration graphs so I want to know how I can find the acceleration due to gravity using the graph. The position graph is the graph of the motion of a ball tossed above a motion detector. The detector used a software to draw a graph and I want to find the force of gravity from this graph, which is the same as the acceleration. Please help!How can I mathematically find the acceleration of an object from the position graph of the object?
Mathematically? Well, there are a number of mathematical operations you can use such as multiplication, addition, substraction...or my favorite: division.How can I mathematically find the acceleration of an object from the position graph of the object?
You're graph looks like a parabola, right?


The easiest way do this is to set your reference height (origin of your graph) at the maximum of the parabola. If you've taken algebra 2, you should be able to determine the equation of a parabola just from its graph.


If you don't remember, here's a refresher:


The equation of a parabola has the form: y-k=a(x-h)^2.


k and h refer to the vertex of the parabola. If you've set your reference axis so that the vertex is at the origin like I suggested above, h and k should equal zero.


Now you have y=ax^2.


All that's left to do is solve for a. This is easy, just pick another point on the graph and plug those coordinates into this equation and solve for a.


If gravity still works, your a number should come out to about 4.9. Differentiating this equation twice will yield a constant acceleration value of two times the value that you found for a...probably about 9.8 m/s/s with some margin of error for air friction, etc.
the derivative of it's position with respect to time should give you velocity and take the derivative of the velocity with respect to time will give you the acceleration
distance = 0.5*A*T^2





Start at:





Time = 0


Distance = 0





Measure a time, say 5 seconds





Measure the distance the object moved in that 5 seconds, say 10 meters





then





10 m = 0.5A*5^2


10 = 0.5*25*A





A = 10 / (12.5)





A = 0.8 m/s^2