Question 5

Item 5 In a ballistocardiograph, a patient lies on an extremely low friction horizontal table. At each heartbeat, a volume of blood is accelerated by the heart toward the head along the ascending aorta. In response, the patient's body recoils in the opposite direction. This motion is detected by sensitive accelerometers attached to the table. (The table is then brought to rest Figure 2 4 6 10A graph of acceleration of the table versus time, termed a ballistocardiogram, is generated. Based on these measurements, the acceleration of the blood ejected by the heart can be determined. Patients with low blood accelerations generally have weakened heart muscles. A sketch of a single cycle of a ballistocardiogram is given in the figure. (Figure 1). The units of the graph are arbitrary and linear for both time, t, and acceleration, a. Part A At what time (in the arbitrary time units of the graph) is the speed of the table (and hence the speed of the blood in the opposite direction) a maximum? > View Available Hint(s) VO AEd ? SubmitA common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity v on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion. however. these vectors have only a Figure Up(m/s) 2.0 1.5 1.0 0.5 1 (8) 0 10 20 30 40 50(Figure 1) is a plot of velocity versus time for a particle that travels along a straight line with a varying velocity. Refer to this plot to answer the following questions. Part A What is the initial velocity of the particle, vo? Express your answer in meters per second. View Available Hint(s) AEd ? Un= m/s SubmitPart B What is the displacement Ax of the particle? Express your answer in meters. View Available Hint(s) VO AEd AT = m SubmitPart C What is the average acceleration day of the particle over the first 20.0 seconds? Express your answer in meters per second per second. View Available Hint(s) 0 AEd O ? m/$2 SubmitPart D What is the instantaneous acceleration a of the particle at t = 45.0 s? View Available Hint(s) O 1 m/s O 0.20 m/$2 a = 0-0.20 m/s- O 0.022 m/s- O -0.022 m/s' SubmitNow that you have reviewed how to plot variables as a function of time, you can use the same technique and draw an acceleration vs. time graph, that is, the graph of (instantaneous) acceleration as a function of time. As usual in these types of graphs, time & is plotted on the horizontal axis, while the vertical axis is used to indicate acceleration a. Part E Which of the graphs shown below is the correct acceleration vs. time plot for the motion described in the previous parts? A 0, (m/s?) 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 10 20 30 40 50' (5) -0.05 10 20 304050* (9) -0.05 -0,10 -0.10 -0.15 -0.15 -0.20 -0.20 D a, (m/s) a, (mis) 0.20 0.20 0.15 0.15 0, 10 0.10 0,05 0.05 10 20 30 47 50* 1 (5) -0.05 -0.05 10 20 30 40 50 * (s) -0.10 -0.10 -0.15 -0.15 -0.20 -0.20 View Available Hint(s) O Graph A O Graph B O Graph C O Graph D SubmitV Part A A dragster starts from rest and accelerates at 17 m/s'. How fast is it going after t = 4.0 sec? Express your answer in miles per hour. VO AEQ ? U= mph Submit Request AnswerPart A To take off from the ground, an airplane must reach a sufficiently high speed. The velocity required for the takeoff, the takeoff velocity, depends on several A plane accelerates from rest at a constant rate of 5.00 m/s' along a runway that is 1800 m long factors, including the weight of the aircraft and the Assume that the plane reaches the required takeoff velocity at the end of the runway. What is the time wind velocity. tro needed to take off? Express your answer in seconds using three significant figures. View Available Hint(s) tTo = 26.8 s Submit Previous Answers Correct If you need to use the answer from this part in subsequent parts, use the unrounded value you calculated before you rounded the answer to three significant figures. Recall that you should only round as a final step before submitting your answer.Part B W What is the speed vro of the plane as it takes off? Express your answer numerically in meters per second using three significant figures. View Available Hint(s) UTO = 134 m/s Submit Previous Answers Correct If you need to use the answer from this part in subsequent parts, use the unrounded value you calculated before you rounded the answer to three significant figures. Recall that you should only round as a final step before submitting your answer.Part C What is the distance dfirst traveled by the plane in the first second of its run? Express your answer numerically in meters using three significant figures. View Available Hint(s) dfirst = 2.50 m Submit Previous Answers V Correct If you need to use the answer from this part in subsequent parts, use the unrounded value you calculated before you rounded the answer to three significant figures. Recall that you should only round as a final step before submitting your answer.Part D w What is the distance dlast traveled by the plane in the last second before taking off? Express your answer numerically in meters using three significant figures. > View Available Hint(s) dlast = 132 m Submit Previous Answers V Correct Since the plane is accelerating, the average speed of the plane during the last second of its run is greater than its average speed during the first second of the run. Not surprisingly, so is the distance traveled. If you need to use the answer from this part in subsequent parts, use the unrounded value you calculated before you rounded the answer to three significant figures. Recall that you should only round as a final step before submitting your answer.Part E What percentage of the takeoff velocity did the plane gain when it reached the midpoint of the runway? Express your answer numerically to the nearest percent. View Available Hint(s) 71 % Submit Previous Answers V Correct This is a "rule of thumb" generally used by pilots. Since the takeoff velocity for a particular aircraft can be computed before the flight, a pilot can determine whether the plane will successfully take off before the end of the runway by verifying that the plane has gained 71% of the takeoff velocity by the time it reaches half the length of the runway. If the plane hasn't reached that velocity, the pilot knows that there isn't enough time to reach the needed takeoff velocity before the plane reaches the end of the runaway. At that point, applying the brakes and aborting the takeoff is the safest course of action.Item 10