CAPM Challenge - Rolling Ball Acceleration

Introduction:
For this challenge, our physics class was tasked with finding the acceleration of a ball rolling down a table. We were allowed to use a ball, chalk, and a ruler. We also had to fined the instantaneous velocity of the ball at 4 seconds.

Procedure:
We are going to have a ball on the table(inclined). We will mark the position of the ball at each half second with the chalk and will measure with the ruler. We predicted that there will be a constant acceleration of the ball.


Raw Data:
This data came from an average of three trials, and is converted from originally cm to m.

Time(s)     Position(m)
.5               .056
1                .148
1.5             .283
2                .466
2.5             .682
3                .905

Evaluation of Data:
Originally, we found the x vs. t graph, but we changed it to be x vs. t^2 because that linearized the graph and gave us the equation for the line. We used this data to find the acceleration of the ball. Our equation from the x vs. t^2 Graph was:
Position=.0973(time)+.0546
We were able to use this equation to find our predicted acceleration of the ball.
Acceleration = 0.1946 m/s^2

This graph shows the position vs. time^2 graph after we manipulated the data

This graph shows the position vs. time from our raw data.

Conclusions:

From this lab we have used our learning from class, and applied it to the real world. We took data using only a ball, a ruler and chalk, and were able to calculate the acceleration of the ball. Our error margin was within ten percent also, which shows our knowledge of this material.