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Introductory Physics Hunter CollegePosition and VelocityObjectives: Students will learn how position relates to constant velocity by predicting positions and velocities of given position vs. time and velocity vs. time graphs. Students will also calculate the slope of position vs. time graph to calculate the velocity. Finally, students will determine position from the equation x(t) = v0 t + x0 .BackgroundAny measurement of position, distance, or speed must be made with respect to a reference frame. For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher. For today’s simulation we will use the cartesian coordinate plane, xy-axis, to orient our frame of reference.Distance vs. Displacement Displacement (blue line) is how far the object is from its starting point, regardless of how it got there. Displacement depends on direction and thus, is a vector quantity; it can be a negative, or positive value that indicates its direction and magnitude.The displacement is written: ?x = x2 ? x1Distance traveled (dashed line) is measured along the actual path. Distance is a length, and is thus a scalar quantity. Distance can be any measure x ≥ 0 units.Average Speed vs. VelocitySpeed is how far an object travels in a given time intervalVelocity is speed and includes directional information. For constant velocity, non-accelerated motion, we can use the equation v = ?x/?t to solve for either position, or velocity, or time, if we know the other quantities .Pre-Lab QuestionsConsider a deer that runs from point A to point B. The distance the deer runs can be greater than the magnitude of its displacement, but the magnitude of the displacement can never be greater than the distance it runs.TrueFalseConsider a car that travels between points A and B. The car's average speed can be greater than the magnitude of its average velocity, but the magnitude of its average velocity can never be greater than its average speed.TrueFalseComplete the partially filled in table belowPhysical QuantityScalarVectorPositiondisplacementMotionTimeSeconds/hours/minutesNAProceduresGetting StartedGo to We will use this Physics Simulation to practice with non-accelerated motion in 1D. Your screen should look like the image below:Please look at the position vs time, velocity vs time graphs, and the motion diagram, which shows the displacement of motion of the red dot.Notice there are Play, Pause, << Step, Step >>, and Reset tabs you will use throughout this simulation to modify your simulation as it plays. Click Pause, << Step, and Step >> , Reset to change the variables, as necessary.There are 3 sliders that control Initial position (from -50m to +50m), Velocity (from -10m/s to +10m/s), and Acceleration (from -2.0 m/s/s to 2.0 m/s/s). We will keep the acceleration at zero for all of today’s simulations.Under the 3 sliders there are Match a position graph and Match a velocity graph . Today we will use Match a position graph.Graph MatchingReview the 5 different Position vs. time and velocity vs. time graphs below. Predict the velocity that will determine the position for each of the 5 Position vs. time graphs using the controls on the simulation, explained in the Getting Started steps.Go to the simulation Matching Graphs.Click Graph 1, at the bottom of the screen, . Predict how to match this graph by predicting how you should choose the initial position and the velocity values with the sliders at time t = 0 s, 10 s, & 20 s. Note: Each of these graphs may have one to three different values for position and velocity.Press the Play tab to run the simulation, with your predictions.Did you match the graph perfectly? If not, change the Initial position and velocity controls until you have matched the graph. Then record the data from the graphs into the Matching Graphs table below. You may need to pause the simulation to change the velocity at certain times. Use << Step and Step >> tabs to slowly increment the motion in time steps of 0.05s.Repeat steps 8 – 10, for Graphs 2 – 5.Calculate distance, displacement, average speed, and average velocity for each of the 5 graphs you matched; enter your results in the table Matching Graphs.Table: Matching GraphsGraph OneTime t (s)Position x(t) (m)Velocity (m/s)Total Distance (m)Total Displacement (m)Average Speed (m/s)Average Velocity (m/s)t1=0x1= 50 v1= 0t2=20x2=50v2=00 s0 s0 m/s0 m/st3=x3=v3=Graph TwoTime t (s)Position x(t) (m)Velocity (m/s)Total Distance (m)Average Speed (m/s)Average Speed (m/s)Average Velocity (m/s)t1=0x1=0v1=5t2=20x2=100v2=5t3=x3=v3=Graph ThreeTime t (s)Position x(t) (m)Velocity (m/s)Total Distance (m)Total Displacement (m)Average Speed (m/s)Average Velocity (m/s)t1=0x1=-50v1=0t2=10x2=-50v2=+10t3=20x3= +50v3= +10Graph FourTime t (s)Position x(t) (m)Velocity (m/s)Total Distance (m)Total Displacement (m)Average Speed (m/s)Average Velocity (m/s)t1=x1=0v1=5t2=x2=50v2=5t3=x3=-50v3=-10Graph FiveTime t (s)Position x(t) (m)Velocity (m/s)Total Distance (m)Total Displacement (m)Average Speed (m/s)Average Velocity (m/s)t1=x1=50v1=-3t2=x2=20v2=-3t3=x3=20v3=0QuestionsIs there any instance where the total displacement is greater than total distance? Explain.Is there any instance where the average velocity is greater than the average speed? Explain.Motion with Constant Velocity: Now play the simulation, without matching, by selecting the tab at the bottom of the screen, just below the match graph options.Move the Initial position slider to 0m.Move the Velocity slider, to choose any velocity between 1 and 10 m/s.Set the acceleration slider to 0m/s2.Now run the simulation to see how long it will take.Divide the total time of your simulation by 4. Play your simulation again, so that you may now record the position and time for the first quarter of the simulation in the Constant Velocity table below. Continue the simulation until you get to the 2nd quarter, 3rd quarter, and the end of your simulation and record those positions and times in the Constant Velocity table.Take a screenshot of your position graph, after simulation runs completely, and enter it here, like this one:Calculate 2 slopes. The first between 0 and the first quarter of your simulation and the second from third quarter to the end of your simulation.Enter your slope calculations in the Constant Velocity table below:Table: Constant VelocityVelocity [m/s] = Data CollectedCalculate Time [s]Position [m]Slope= Δx/Δt [m/s]0t0 = 0x0 = 01t1 = x1 =(Δx/Δt)1 =2t2 = x2 =3t3 = x3 =(Δx/Δt)2 =4t4 =x4 =(Δx/Δt)avg =Compare the average slope with the velocity, i.e. calculate the percent error between the velocity and your calculated average slope.Now calculate the position, x2calc, value using your recorded data from the Constant Velocity table and the equation x2calc(t) = vt + x0. Enter your results in the Position Data table below:Table: Position DataGraph Position XgraphCalculated Position XcalculatedPercent Error Xcalculated vs. XgraphX2graphx2calcCompare x2calc with the value x2 from your data, i.e. calculate the percent error, for your calculated position vs. your measured position.Repeat steps 21 for 2 more positions; choose any 2 positions you like.Post-Lab QuestionsThe figure shows a graph of the position of a moving object as a function of time. What is the velocity of the object at each of the following times?At t = 1.0 sAt t = 2.5 sAt t = 4.0 sAt t = 5.5 sWhat is the average velocity of the object from t = 0 s to t = 4.0 s?What is the average velocity of the object from t = 0 s to t = 6.0 s?The graph in the figure shows the position of an object as a function of time. The letters H-L represent particular moments of time.At which moment in time is the speed of the object the greatest?At which moment in time is the speed of the object equal to zero?If you run a complete loop around an outdoor track of length 400 m in 100 s, find youraverage velocity and average speed.A polar bear starts at the North Pole. It travels 1.0 km south, then 1.0 km east, and then returns to its starting point. This trip takes 0.75 hr. What was the bear's average speed? What was the bear's average velocity?Two locomotives 70 kilometers apart are travelling on the same track towards each other , Engine A? moves at? 22 kilometers per hour east? and engine B moves at 13 kilometers per hour west.? At the instant both trains begin moving, an annoying mutant fly begins flying from engine A? towards engine B at 33 kilometers per hour . The instant it touches B, it turns around and flies back. It goes on? this way until the two locomotives collide and the mutant fly is finally squashed.?So, before its untimely demise, determine? the following:the total distance the fly flewthe time it took till? it was eliminatedThe average velocity of the fly?? ................
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