Kinematics/calculating a line from a curve?

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Homework Help Overview

The discussion revolves around a kinematics problem where a student is attempting to determine the acceleration due to gravity (g) by analyzing the relationship between distance fallen and time taken for a ball dropped from various heights. The provided data indicates a non-linear relationship, prompting the need to identify a way to graphically represent it as a linear relationship.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring how to transform the given data, which yields a curve, into a linear format suitable for graphing. There is a focus on identifying the correct quantities to plot in order to achieve a linear relationship.

Discussion Status

Some participants have suggested using the equation D=1/2gt² and transforming it into a linear form, while others are seeking clarification on what specific variables to plot to achieve this linearity. The conversation indicates an ongoing exploration of different interpretations and approaches without reaching a consensus.

Contextual Notes

There is uncertainty regarding the interpretation of the problem statement and the specific requirements for graphing the data. Participants are questioning the assumptions about the relationship between distance and time in the context of the experiment.

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Homework Statement


"If only the variables D and t are used, what quantities should the student graph in order to produce a linear relationship between the two quantities?"

The data:
distances (m): .1, .5, 1, 1.7, 2
Time(s): .14, .32, .46, .59, .63

Basically, a student is dropping a ball from several points and recording how long the fall took from each point. They're trying to experimentally determine g. So the data yields a curve. The full problem is here, it's the first one after the reference sheet: http://apcentral.collegeboard.com/apc/public/repository/_ap06_frq_physicsb_fo_51783.pdf


Homework Equations


n/a

The Attempt at a Solution


I'm not exactly sure what the question is asking. Since the data gives a curve, but I need a line, The "quantities" they want are the end points of the line segment that approaches all the points in the curve the most, right? How do I get that?

I tried graphically, this is the best I could get:
j9n02q.jpg


But there's got to be a math way to do it. Please help... :rolleyes:
 
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Well you know that

D=ut+1/2at2 which simplifies to D=1/2gt2

You can plot appropriately to get a straight line.
 
I'm sorry to seem so dense but- what do you mean? what do I plot? D=1/2gt^2 is still a curve...
 
fruitbowl said:
I'm sorry to seem so dense but- what do you mean? what do I plot? D=1/2gt^2 is still a curve...

If you make the equation into the form Y=MX+C and plot Y vs. X you will get a straight line. Put Y=D, what should X be to get a straight line?
 

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