Acceleration information from the data collected with MacMotion

KEY POINT: Remember that the sonic ranger only really gives the position of an object every time interval. But what you probably care about is the acceleration. Below are two different methods for determining the acceleration from your data. Hopefully, you have already made a graph with only the "good" points.

Method 1: Using the position data (distance versus time graph).

• First, if you are finding the acceleration then you are probably assuming it is a constant acceleration. If this is the case, the well known kinematics equations apply
• . • From this, you can see the relationship between x and t. So if you have a graph of x vs. t, you can add a trendline that looks like the equation:
• • This says that the relationship between x and t should be a 2nd order polynomial. This gives a hint as to what kind of trendline to add in Excel (i.e. a second order polynomial). So, let's do that ...add a second order trendline to our data (and include the equation on the chart)
• • I hope you remember that Excel is not very smart - it does not properly label the trendline equation. It says y instead of x and x instead of t - but that's ok. Excel says that the number infront of t^2 is 1.4121. According to the kinematic equation, the number in front of the t^2 term is 1/2 a - so 1/2 a = 1.4121
• • So, 1/2 a = 1.412 so then a is 2*1.412 =2.824 - thus we have obtained the acceleration from the position graph.

Method II: Using the velocity versus time graph