CAPM Challenge Problem

This is a sketch of how our setup looks like. The green objects represent the books under the table, with the table being the black line. The orange object is our metal ball, which rolls faster when rolling down the table (look for the red arrows). We measure our spacing in centimeters, timed to half-seconds for the most accurate measurements. 

     

0	0
0.5	5
1	16
1.5	32.5
2	54
2.5	80
3	110
3.5	144

Our raw data looks like this, with the x-coordinate being the half-seconds we measured and the y-coordinate being the distance we measured in centimeters.

Our first graph shows our raw data in a position versus time graph, proving our guys correct that our object would move with an exponentially increasing speed. We were originally going to use this data and create a Velocity vs. Time then find the slope of that line. That would then give us the acceleration of our ball. However, we could easily cut down on the number of steps to do by instead using a Position vs. Time Squared graph.

This is the result of squaring our time and using the new results instead of the old time, which turns our exponential data graph into a straight line that has a slope. The equation for this line is equal to X=1/2 at^2, with the slope of this line being equal to a half of the acceleration of the object. Our slope, as seen in the graph above, is equal to 11.708 cm, or .11708 meters. we took our new slope and multiplied it by 1/2, which turned out to look like this: .11708/1*2/1. This all resulted with our acceleration being equal to .23416 meters/second squared.