kinematics

# kinematics - Measuring Motion walk back and forth in front...

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Measuring Motion walk back and forth in front of Motion Detector Objective: To understand the relationship between Distance, Velocity and Acceleration . To gain familiarity with collecting position data using a computer, motion sensor and lab interface. To be able to read and interpret a one-dimensional motion graph and to make predictions using Kinematics (equations of motion). To perform data analysis to non- repetitive measurements (find a pattern in the data). Apparatus: Computer, motion sensor, LabPro lab interface, meter stick, flat reflective surface (folder or book), Pasco track, Pasco cart. Introduction Kinematics allows to describe motion mathematically and make predictions of subsequent motion, such as an object's position or velocity at some future time. Such skills are vital in any field that deals with moving objects, and that includes just about all branches of science and engineering. For instance, in Forensic Science one can calculate how fast a car was moving by measuring the length of the skid marks at an accident site. In Civil Engineering, the length of an airport runway is determined with Kinematics from such values as the speed of the plane at takeoff, and the acceleration of the plane. Galileo Galilei (1564-1642) performed experiments similar to those you will do today to discover the laws of Kinematics. Unlike he, who used crude instruments (such as using his pulse as a stopwatch), you will be using a much more sophisticated device that you are already familiar with – a motion sensor – to track the motion of an object. Theory Kinematics As you learned in lecture, Distance, Velocity and Acceleration are related to each other as follows:

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1. Distance (always positive) is the length of travel. In this experiment, it is the length of travel before reflection of sound waves emanating from the motion sensor. Displacement is the change in distance x = x f x i , and can be both positive or negative. 2. Average velocity is the change in displacement divided by change in time v = x t . The slope between any two points in the x vs. t plot is the average velocity. 3. Average acceleration is the change in velocity divided by change in time a = v t . The slope between any two points in the v vs. t plot is the average acceleration. In the limit where the time interval between two points goes to zero t 0 , the above quantities become instantaneous velocity and acceleration and can be written in derivative form: v = dx dt ; a = dv dt In the first experiment, you will be the object in motion. You will try to duplicate, by moving back and forth in front of a motion sensor, various plots of Distance, Velocity and Acceleration versus time. These graphs will be automatically plotted in the data- acquisition software, Logger Pro.
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