Sn t cm s 0 0 0025 6036 0050 8432 0075 10876 0100

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∆Sn ∆t ( cm s ¿ 0 0 0.025 60.36 0.050 84.32 0.075 108.76 0.100 135.12 0.125 156.04 0.150 183.00 0.175 206.08 0.200 230.36 0.225 255.52 0.250 281.96 0.275 302.44 0.300 332.12 0.325 345.68 0.350 375.56 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 f(x) = 969.27x + 48.76 R² = 1 Velocity vs Time Time (s) Velocity (cm/s)
The instantaneous velocity-vs.- time graph can be represented by the equation for the straight line: v = v 0 + at Where v 0 is the initial velocity (the velocity at t = 0 ), and a is the acceleration due to gravity (g). On the graph, v 0 is the intercept on the velocity axis of the v-vs.-t graph and the acceleration is the slope of the straight line. 2
0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 f(x) = 478.13x^2 + 51.98x - 0.12 R² = 1 Displacement vs Time Time (s) Distance (cm) Table 2: Instantaneous Velocities t (at midpoints) (s) V*(cm/s) v ( from table 1 ) (cm/s) 0.1125 173.3 156.04 0.2625 275.0 214.8 Discussion: According to the data gathered and analyzed, the value of the acceleration obtained by determining the value of the slope of the velocity vs. time graph ( 9.69 m/ s 2 ), is almost the same as the accepted value of gravity, which is known to be 9.81m/ s 2 . The value of gravity obtained from the experiment is lesser than the actual value is due to inevitable imprecision in measurement on the values obtained, environmental factors such as air resistance to the free falling object, incomplete definition when different people measure the same thing, instrument resolution, and parallax error, throughout out the experiment. %Error = 9.81 9.69 9.81 × 100 = 1.24% Conclusion: In this experiment, according to the rate measured at which the velocity changed with time, the acceleration of a free falling body is due to gravity (g)
Questions: 1. The accepted value of g is 9.81m/ s 2 while the obtained value from the velocity-time graph is 9.69m/ s 2 . The difference between the two values is 0.53m/ s 2 . One of the sources of the experimental uncertainty is incomplete definition where different people