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III. Discussion and Analysis
Part 1: Newton’s First Law
The velocity of the cart on the way to the barrier will be compared to the velocity of the cart on
the return trip to the CBR. First, the velocity of the cart on the way to the barrier was found by
inserted a line of best fit into the data of distance/time for that defined time period.
The slope of
this line is the value of the velocity. The graph below shows the velocity bestfit line with the
associated error in the values of distance and time.
Fig. 1: Distance/time plot in the time frame from 2.598493 s to 3.29887 s (as cart was traveling
from CBR)
The velocity for the cart on the way to the barrier from the CBR unit is found by the slope of this
bestfit line. The bestfit line has a R
2
value of 0.998 which ensures its accuracy in the defined
point set. The velocity (the slope of the line) is 0.845 m/s.
Fig. 2: Distance/time plot for the time frame from 3.29987 s to 4.797218 s (cart traveling back to
CBR)
This graph displays the data collected after the CBR hit the barrier in the track and as it returns
closer to the CBR unit.
The velocity during this time section is found to be 0.4003 m/s as found
by the slope of the bestfit line that has an R
2
value of 0.9972.
The data for this section has the
same uncertainties in distance and time as those of Fig. 1 as previously described.
Error Analysis and Propagation for Part 1:
1. The CBR itself lends certain uncertainty to the measurements in question. The time
uncertainty was +
the time between the CBR beeps. These beeps are the mode by which the CBR
calculates the distance.
The distance between our time beeps was found by taking the t value at
time 2 and subtracted the t value at time 1:
=

δt t1 t0
= .
 = .
δt 0 199884 0 0 199884 s
This was our uncertainty in time sprouting from the CBR equipment use.
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View Full Document2. The distance uncertainty is 1% of the total distance from the CBR as explained in the CBR
manual and the provided Appendix B (Ellis, 2009). Therefore, the uncertainty in d increases
directly as the distance from the CBR increases.
3. The uncertainty in velocity was calculated by taking the v
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 Fall '08
 McAdams
 Physics

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