Like I said, I am only a little cart trying to figure out how fast I can accelerate. So my proud renter took me, and put me on a track, measured every half second, and then took data to see first my change in position over time, which lead to velocity, and then solved for acceleration.
This looked like the initial chart of:
This gave us the following graph. Note the curve upward.
We had to take the following formula, y=mx+b, and change it into a line that more closely resembles the formula's we are dealing with. The following formula is x=slope*t^2+xo. When you notice that the t is squared, it is because the time must be squared to fit into a graph to solve for acceleration.
This produced the following graph:
Note the slope of 0.070747.
In order to solve for Acceleration, we use the formula V=1/2a
Thus, as our slope is velocity, we can multiply it by 2 and solve for the acceleration.
Our acceleration is 0.070747*2=0.141494.
However, when we checked it with the motion detector, it found .22 as the slope. I do not know why, but will continue to ponder why I (the cart) am not accelerating at the indicated pace.
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