1. Graphical Analysis: Motion



1. Graphical Analysis: MotionGuided InquiryDriving Question | ObjectiveHow are the graphs of position versus time, velocity versus time, and acceleration versus time of an object undergoing constant acceleration related? Experimentally determine the relationships between the graphs of position, velocity, and acceleration versus time for an object undergoing constant acceleration, both positive and negative.Design and Conduct Your ExperimentIt is your group’s responsibility to design and conduct an experiment whose data will support your answer to the driving question above. Use the answers to the guiding questions below to help guide your experiment design. After you have answered the guiding questions, write an outline of the equipment setup and procedure you will use to collect data, identifying the steps in sequence and the points at which each piece of equipment will be used.Suggested Materials and EquipmentAlthough you have the freedom to design your procedure using any reasonable equipment at your disposal, the following equipment is recommended for your experimental setup.Data collection systemPASCO Dynamics Track End Stop3PASCO Smart Cart1Meter stickPASCO Dynamics track with feet2Thick text book1ap372ap083ap11PASCO Smart CartPASCO PAStrackPASCO Dynamics Track End StopGuiding Questions1.What equipment will you need to accurately produce a constant-velocity graph? Describe your setup for gathering this data. Be sure you consider the equipment made available to you.2.How could you use a Smart Cart and track to set up a situation that produces a constant (positive) acceleration graph?3.Describe a setup that will demonstrate negative acceleration and produce an accurate graph of this motion.4.If the change in position of the cart with respect to time is equal to the cart's velocity, what does the slope of the position versus time graph represent? Similarly, what does the slope of the velocity versus time graph represent?5.Given a graph of position versus time, describe how you would sketch the remaining two graphs (velocity versus time and acceleration versus time).Experimental DesignYour goal is to experimentally determine the relationships between position, velocity, and acceleration versus time graphs for an object undergoing constant acceleration, both positive and negative. Use the responses to the Guiding Questions to help finalize your procedure and your equipment configuration.Once you are convinced that your procedure will accomplish the experiment's objectives, record your experimental setup and procedure in the following sections. SetupDraw and/or describe your experimental setup such that a third party could recreate the same setup in an attempt to reproduce your experiment?ProcedureOutline the procedure you will use in your experiment, listing all of the steps below. Your outline should be written such that a third party could follow the same procedure in an attempt to reproduce your experiment?Collect DataPerform your experiment and record all relevant data. Present your data below (or in an attached document) in a form that best suits the experiment format, such that a third party can understand your experimental results in an attempt to reproduce them.Analysis Questions1.One of the three types of motion you explored was constant velocity, but was the velocity of the cart totally constant during your trials or did it slow down or speed up slightly? What are some factors that may have caused the velocity of the cart not to be constant? 2.Another type of motion you explored was constant acceleration. What caused the constant acceleration of the cart? How could you have increased this acceleration, and how would your graphs of position and velocity versus time be different if the acceleration was greater?3.Another student moved a Smart Cart with their hand back and forth across the track. Assuming the graph below shows this data, describe the motion of the cart during data collection in terms of its speed and direction.Synthesis Questions1.For each of the two position versus time graphs below, sketch the corresponding velocity and acceleration versus time graphs in the blank axes below each graph. Be sure to label both axes of each graph with the correct scale. 2.Given the velocity versus time graph shown below, sketch the corresponding position versus time and acceleration versus time graphs. (Assume the object starts at x = 0 m at time t = 0 s). Be sure to label both axes of each graph with the correct scale.3.Given the acceleration versus time graph shown below, sketch the corresponding velocity versus time and position versus time graphs. Assume that initial velocity and position at t = 0 s is equal to 0 m/s and 0 m respectively. Be sure to label both axes of each graph with the correct scale. ................
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