A. MEASUREMENTS OF LENGTH The measurements taken for the thickness of a layer are given below. The smallest interval between two scales is 0.01 mm for the instrument that is used. Using the given data, draw the distribution of the data and calculate the average thickness, absolute and relative errors, standard deviation and the experimental probability of each value. Thickness d (mm): 5.97 5.97 6.05 6.06 6.00 6.03 6.00 5.99 5.97 6.01 6.02 5.96 6.00 6.01 6.02 6.01 6.00 6.07 5.98 5.98 6.04 6.05 6.01 6.02 6.03 5.99 5.95 5.95 5.99 5.91 B. MEASUREMENTS OF CONSTANT VELOCITY The position and time values obtained for an object moving with a constant velocity are given below. By plotting the position versus time (x,t) graph on a millimetric graph paper, calculate from the graph: 1) the location of the object at time t = 0 s, 2) the location of the object at time t = 1.5 s, 3) the velocity of the object from the slope, 4) absolute and relative errors of the velocity at times t = 1 s and t = 2 s by using the absolute errors ?x = 0.05 cm, ?t = 0.1 s. t (s): 0.8 1.0 1.2 1.4 1.8 2.0 2.2 x (cm): 5.90 6.55 7.10 7.50 8.50 9.05 9.60 C. MOTION WITH CONSTANT ACCELERATION The position versus time data for an object moving with constant acceleration are given below. Considering the relation x = ½ a t^2, plot (x,t^2) graph and calculate: 1) the acceleration from the slope. 2) absolute and relative errors of the acceleration at t = 0.8 s and t = 1.6 s by using the absolute errors ?x = 0.1 cm, ?t = 0.1 s. t (s): 0.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 x (cm): 0.0 3.6 8.2 14.0 22.8 32.5 44.1 57.2 72.5 89.5
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(2 points) Your task is to estimate how far an object traveled during the time interval 0 ≤ t ≤ 8, but you only have the following data about the velocity of the object. time (sec) 0 1 2 3 4 5 6 7 8 velocity (feet/sec) -4 -3 -1 -2 -3 -4 1 3 1 To get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something like the black curve in the graph below. You decide to use a left endpoint Riemann sum to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is determined by the velocity measurement at the left endpoint of each one-second interval. By using the left endpoint Riemann sum as an approximation, you are assuming that the actual velocity is approximately constant on each one-second interval (or, equivalently, that the actual acceleration is approximately zero on each one-second interval), and that the velocity and acceleration have discontinuous jumps every second. This assumption is probably incorrect because it is likely that the velocity and acceleration change continuously over time. However, you decide to use this approximation anyway since it seems like a reasonable approximation to the actual velocity given the limited amount of data. (A) Using the left endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct units. Total displacement = Total distance traveled = Using the same data, you also decide to estimate how far the object traveled using a right endpoint Riemann sum. So, you sketch the curve again with a black pen and draw rectangles whose height is determined by the velocity measurement at the right endpoint of each one-second interval. (B) Using the right endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct units. Total displacement = Total distance traveled =
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Find the mean of the fluid velocity measurement system assuming that the true value of velocity Vt is 14.0m/s-1
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Question 6: State whether the acceleration is positive, negative, or zero for each of the position functions x(t) in the position versus time graphs below: a) A truck gets on the highway and the driver speeds up to the speed limit and then remains at that speed. Plot velocity vs. time. Label the important events described above. b) Plot acceleration vs. time. Consistency with the velocity plot is part of the grade. Label the important events described above. c) A box falls off a truck driving on the road. So, the driver slows down, stops for a short time and then reverses direction to backup toward the boxes and stops. Plot the truck's position vs. time. d) Plot the truck's velocity vs. time. Consistency with the position plot is part of the grade. Question 8: Three Italian philosophers are debating a hypothesis of motion (similar to a story written by Galileo); when a sailor drops a stone from a tall mast (the tower) of a moving ship where will it fall. To best understand what is happening they choose to ignore air resistance and focus only on these three factors; the ship moves on the sea toward the west at 10 m/s, the Earth rotates at 800 miles/hour to the East, and the stone falls at the rate of g. The three arguments are as follows. a. The first states it will fall at the base of the tower and will not deviate from its path forward or backward. b. The second believes it will fall behind the tower, since the ship is moving forward. c. The third argues it will fall toward the front of the ship due to the earth's rotation. Circle the statement you believe to be true and state your defense using your physics knowledge.
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