Lab #4 - Position Velocity and Acceleration Name Katie Ellis Group Names Eden and Felicia Purpose The group exemplified the relationship between

Lab #4 - Position Velocity and Acceleration Name Katie...

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Position, Velocity and Acceleration 9/27/18 Name: Katie Ellis Group Names: Eden and Felicia Purpose: The group exemplified the relationship between position, velocity and acceleration as velocity being the first derivative and acceleration being the second derivative of the position function. In other words x / ¿ dt v = d ¿ and a = d v / dt , both derivatives taken with respect to time. Procedure: Through the use of a LabQuest2 Data Logger, a motion sensor, dynamics cart and track the group tested these derivative relationships by letting the dynamic cart glide down the dynamic ramp as well as push itself off the bottom of the track. By recording the position v.s time of the cart with the motion detector, we could determine a mathematical model that fit the data taken and reflected through the graphing program Logger Pro. Throughout this lab we tested the accuracy of the mathematical models created by the cart data in which the derivative relation between position, velocity and acceleration was ultimately shown. Data: Task 1: x = 0.08592 t 2 0.06577 t + 0.1377 v = 0.1807 t 0.09312 a = 0.01807 m/s 2 Δ x from 2s (0.348m) to 3s (0.714m) = 0.366m 2.0 3.0 v dt = 0.3677 m Task 2: *below v = 0 m / s x = 0.1281 t 2 0.6102 t + 1.955 v = 0.2532 t 0.6048 a = 0.2532 m/s 2 Δ x from 1.1s (1.438m) to 2.1s (1.238m) = -0.20m 1.1 2.1 v dt =− 0.2026 m *above v = 0 m / s x = 0.08706 t 2 0.4183 t + 1.73
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v = 0.1736 t 0.4171 a = 0.1736 m/s 2 Task 3: Δ x from 0.05s (0.748m) to 1.0s (0.708m) = -0.04m 0.05 1.0 v dt =− 0.03726 m Δ x from 2.05s (0.870m) to 3.0s (0.454m) = -0.416m 2.05 3.0 v dt =− 0.4450 m Analysis: In this lab the group explored and exemplified the derivative and antiderivative relationships between position, velocity and acceleration. By consistently observing the position v.s time and velocity v.s time graphs of motion scenarios where there was a constant acceleration, we could identify this constant acceleration through taking the derivative of the velocity function. This means that the acceleration (when constant) is just the slope of the velocity model. This relationship also applies to the position graph as it can be used to find the velocity function in relation to time through taking the derivative. To find the constant acceleration we’ll use task 1 as an example: we used the equation a = d v / dt where the linear model of best fit was v = 0.1807 t
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  • Spring '15
  • Farris

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