4. Graphical Analysis: Instantaneous Velocity as a function of Time Read the graphing instructions from the syllabus or course resources before you begin. Your data gives the average velocity, not the instantaneous. This could be a problem. However, the mean-value theorem of calculus offers a solution. For constant slope intervals, the average value of the function is the same as the instantaneous value of the function at the midpoint of the interval. 50, vavgzvmsmmm when t=0.05 s, 0.15 5, etc. Q5. Use a Cartesian coordinate system to graph the instantaneous velocity of the glider as a function of time. Place the y-axis about one-third of the way from the left edge of the paper. Draw a best-fit line to your data and extend the line all the way to the time axis where v = 0. Note the point where your line crosses the velocity Physics 195: Linear Kinematics Page 3 0f 8 axis when t=0. This intercept gives the velocity of the glider at the arbitrary time chosen by your instructor. Record this value as v, on your graph. Q6. Use your best-fit line from your graph and obtain the glider acceleration from the slope. Show your work with units on the graph and transfer the result to Data Table Three as am. Q7. Use xf=0+v';xt+%a:v,t2 , and substitute your values from Q5 and Q6 to to predict the position of the glider when t = 1.0 seconds. Show your work with units. Compare your result to the value in your data table for t = 1.0 seconds and calculate the percent difference or error (as appropriate) between this value and the data table value for the glider's position when t = 1.0 second. Show your work with units. Q8. From the principles of calculus, the integral of the velocity function gives the displacement of the object. Use the information from your graph to construct the velocity function describing the motion of the glider. Integrate and evaluate the integral from t=0 to t=1 second to obtain the predicted displacement of the glider. Show your work with units and label the result xp. Q9. From geometry we know how to calculate the area of regular objects. Calculate the area bounded by the axes, the velocity function and the t=1 second line using simple geometric relationships, not by integration. Show your work with units. This is also the displacement of the glider. Label this value xg. Q10. Calculate the percent difference or error (as appropriate) between XP and xg. Show your work with units. D. POSIEIOH as a runcuon OI Ilme (Logaritnmic scale) Read the graphing instructions from the syllabus or course resources before you begin. A simple log-log plot requires that the initial velocity of the glider be zero. The initial position of the glider must also be known. To correct your position and time values, examine the graph of instantaneous velocity as a function of time. When you extend the line of best fit down to v = 0 you see that the glider velocity is zero at a time 'before zero.' Q11. This time interval represents the time between when the glider was released from rest and the data point that your instructor arbitrarily chose. Record it as a positive number, Tc on the Velocity vs. Time graph. Now add Tc to each of the time values from Data Table Two. Record the results as tc (the corrected time) where t + Tc = t:. Q12. To find the actual position of the glider relative to the release point, use the displacement equation with initial position and initial velocity of zero. Use the amt value from Data Table Three and calculate how far the glider moves during the interval Tc. Show your work with units. This is Xc. Add Xc to each of the position values in Data Table Two. Record the result as X: (the corrected position) where x + X: = xc. Since the graph from Q5 shows a non-linear relationship between position of the glider and elapsed time we propose a solution of the form xc = th\". Q13. Column xc now represents the actual position of the glider as a function of time after it was released. Construct a graph of the position of the glider as a function of time using logarithmic scales for both axes. Draw a bestfit line through your data 3. Graphical Analysis: Position as a function of Time (Cartesian scale) Read the graphing instructions from the syllabus or course resources before you begin. Use a Cartesian coordinate system to graph the position of the glider as a function of time. Draw a smooth curve passing through the bulk of your data. Draw a line tangent to the curve at t=0.4 seconds. Draw a second tangent line at t=1.0 seconds. The slope of each tangent line is the instantaneous velocity of the glider at that particular time. Q3. Calculate the slope of each tangent line with units on the graph. Make the lines long enough to accurately determine the slope. V1.0_ V0.4 4. *2 Q use lal 1.030.43 Show your work with units on the graph and transfer the result to Data Table Three as am. to calculate the glider acceleration based on your graph