RipStik accelerated motion

In a previous article I shared the use of a RipStik in SC 130 Physical Science to demonstrate linear constant velocity motion. The ability to generate a relatively constant velocity by swizzling at a constant rate on level ground was useful to that demonstration. 

Today I first introduced the calculations necessary to determine the acceleration as the change in velocity divided by the change in time. I used a hypothetical example where the acceleration was 2 m/s² thus y = x². I made a table time (s) versus distance (m) with x-values at 0, 2, 4, 6, and 8 seconds. I squared the times to generate artificial distances. 

I used the table to calculate the velocity from zero to two seconds and from six to eight seconds. I then used the two velocities and the overall time difference to calculate the average acceleration.

With this example given in class, I moved to the porch to generate actual data.
Annabelle watches as I explain what I am about to do

I began by explaining the set-up. The previous week I had measured the inter-pillar distance at 4.6 meters. As in the summer, I planned to use the full length of the porch to generate more data than the two points I had recorded last spring. This is in part a reflection of my increased confidence and ability on the RipStik. I have more control over my acceleration and a higher top end than I could attain last spring.

In my right hand is a chronograph
 I began slowly, gradually building up speed. Monalisa appears doubtful on the right.

As I passed each post I clicked on a lap timer that was keeping track of both lap and split times
I returned from the far end of the porch confident of a new final velocity. Adam on the right.
In this demonstration I accelerated the RipStik from rest over a distance of 36.8 meters. Data from the run is recorded in the first two columns below.

Time (s) Distance (m) dtheor (m) v (m/s) a (m/s²)
0 0 0 0 0.18
5.08 4.6 2.84 0.91 0.18
8.18 9.2 7.37 1.48 0.19
10.64 13.8 12.47 1.87 0.16
12.41 18.4 16.96 2.6 0.41
14.26 23 22.39 2.49 -0.06
16.04 27.6 28.33 2.58 0.05
17.29 32.2 32.92 3.68 0.88
18.28 36.8 36.8 4.65 0.98

Distance-theoretic is a crude calculation using only the 18.28 seconds, 36.8 meters data point to determine the coefficient for d = ½ a t². As my acceleration was not truly constant, this is not the best fit quadratic. That said, the coefficient suggests an acceleration of 0.2203 m/s².

The students were to work out the average acceleration from the speed between the first two posts (0.91 m/s) and the last two posts (4.65 m/s), using the time difference between 18.28 seconds and 5.08 seconds. This yields an acceleration of roughly 0.28 m/s². 

The table reveals that from 12 seconds to 16 seconds my acceleration dropped to a deceleration briefly. My velocity was briefly fairly constant.

Graph of time, distance, velocity, and acceleration data
Last spring I attained a peak speed of 1.78 m/s over a 9.2 meter swizzle. This past summer I hit 2.43 m/s over a 19.52 meter swizzle. This term I reached an estimated 4.65 m/s at the end of 18.28 meters. That said, there is likely little upside left as at 4.65 m/s on level ground I am swizzling just as fast as I can drive my legs. And I then have to jump off at the end at a speed nearly double my normal jogging speed.

The exercise always holds the rapt attention of the students. The result is perhaps a more traditional homework, but having the students attempt to do the riding would surely send the bulk of the class to the dispensary for scrapes, bruises, sprains, and possible fractures. None of the students admitted to being able to ride a RipStik, and given what I know of my students outside of class, I am rather confident that they are being honest with me.

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