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Free Fall


             II. Data and Calculations.
             i ∆xi (cm) ∆ti (s) ti (s) cm/s.
             1 4.552 .04 .02 113.45.
             2 6.116 .04 .06 154.15.
             3 7.789 .04 .10 194.725.
             4 9.314 .04 .14 252.85.
             5 11.102 .04 .18 277.55.
             6 12.454 .04 .22 311.35.
             7 14.002 .04 .26 350.05.
             8 15.556 .04 .30 388.5.
             9 17.134 .04 .34 428.35.
             10 18.774 .04 .38 469.35.
             11 20.186 .04 .42 504.65.
             The above table shows the raw data for trial one.
             The average velocity for the interval is calculated as :.
             = ∆ x i = 4.552 cm.
             D D D D D = 113.75 cm/s.
             ∆ ti 0.04 s.
             Below is the table for the second trial .
             i ∆ xi (cm) ∆ ti (s) Ti (s) cm/s.
             1 3.201 .04 .02 80.025.
             2 4.779 .04 .06 119.48.
             3 6.482 .04 .10 162.05.
             4 8.164 .04 .14 204.10.
             5 9.580 .04 .18 239.50.
             6 11.157 .04 .22 278.93.
             7 12.690 .04 .26 317.25.
             8 14.299 .04 .30 357.48.
             9 15.834 .04 .34 395.59.
             10 17.419 .04 .38 435.48.
             11 18.906 .04 .42 472.65.
             12 20.538 .04 .46 513.45.
             The velocities at certain time intervals which follow the best fit line is obtained by:.
             Y = v fit = 977.39 x + 96.40.
             V fit = 977.39 (0) + 96.40 = 9.6403 áÁ 101 .
             The table below summarizes the above calculations for trial 1 and 2, for velocities at different time intervals, the velocity according to the best fit line, and their difference.
             Time (s) V fit ( cm/s) V fit - (cm/s).
             00 96.40 n/a.
             02 1.1595 x 102 2.1511.
             04 1.5505x 102 .08968.
             08 1.9414 x 102 -.05825.
             10 2.3285 x 102 0.3882.
             18 2.7755 x 102 -5.2161.
             22 3.1143 x 102 0.0795.
             26 3.5005 x 102 0.4752.
             30 3.8962 x 102 0.7209.
             34 4.2872 x 102 0.3666.
             38 4.6935 x 102 -1.5377.
             42 5.0691 x 102 2.2580.
             The table below summarizes the calculations for trial 2.
             Time (s) Vfit (cm/s) V fit - (cm/s).
             00 62.82 n/a.
             02 82.42 2.3933.
             06 1.2162 x 102 2.1434.
             10 1.6082 x 102 -1.2316.
             14 2.0002 x 102 -4.0815.
             18 2.3922 x 102 -0.2814.
             22 2.7842 x102 -0.5063.
             26 3.1725 x 102 0.3688.
             30 3.5748 x 102 -0.6561.
             34 3.9585 x 102 0.1690.
             38 4.3548 x 102 -0.2559.
             42 4.7265 x 102 1.7691.
             46 5.1362 x 102 0.1692.
             The table below summarizes the calculations for the delta, sigma, initial velocity, and the uncertainty of the acceleration and the uncertainty for the initial velocity for both trials.


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