Solve Gravity Lab Problem: Determine Accel Due to Gravity

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To determine the acceleration due to gravity from the quadratic fit equation y=4.97x^2+1.53x+0.0503, the coefficient 4.97 represents half of the gravitational acceleration. This indicates that the acceleration due to gravity is approximately 9.94 m/s², which is slightly higher than the standard value of 9.8 m/s². The initial velocity, represented by the coefficient 1.53, is interpreted as 1.53 m/s. The discussion highlights the importance of correctly identifying the variables in the equation, with some participants noting preferences for notation clarity. Overall, the approach to solving the problem aligns with standard physics equations for motion under gravity.
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Homework Statement


Suppose that a quadratic fit to a position plot yields the following fit result: y=4.97x^2+1.53x+.0503, how would I determine the accelearation due to gravity?





Homework Equations


I know that y=1/2gt^2+Vnaught(t)+ynaught. I know that g is 9.87m/s^2. So in my original given equation, I know that 4.97 is half of the gravity, and 1.53 is my Vnaught. Would this be the answer they are looking for, or is there something I am missing?


The Attempt at a Solution


I may be exploring this question deeper then I should. I believe that the acceleration due to gravity is 9.8m/s^2, and the initial velocity of the particle would be 1.53m/s?
 
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Nope, you have the right idea (though I for one wouldn't have written the initial equation as y = 4.97x^2+1.53x+.0503 - I would have written it as y=4.97t^2+1.53t+.0503, but that's just me being picky.)
 
That is just the way the lab gave the initial equation. I am working on my preliminary assignment. So I haven't actually done the problems yet.
 

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