Name: Period: Due Date: AP Physics 1 Homework - Representing Motion 1. A world-class runner can complete a 100-m dash in about 10 seconds. A team of sports scientists are studying the motion of a particular runner. The scientists take a video of the runner completing the 100-m dash, and then use the video to determine the distance the runner has traveled from the start of the race every second. The distance data has an error range of 0.3 m, meaning that two values that are less than 0.3 m apart should be treated as equal. The data are shown below. Time (s) 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Distance (m) 0.0 1.5 6.1 13.7 24.4 4 36.9 49.5 5 62.2 74.8 87.4 100.0 (a) At what time does the runner approximately quit accelerating and begin to move with constant speed? Explain how you arrived at your answer. (b) Calculate the runner's average speed for the entire race. (c) Estimate the runner's constant velocity after acceleration ceases. (d) Without discussing specific numbers, explain why your answer to part (c) is greater than your answer to part (b). Your response should show understanding of average and instantaneous velocity.AP Physics 1 Homework - Representing Motion (e) Plot a graph of the runner's position as a function of time. 100 90- - - . . . . . .3- . . . . . . . . - - . . . . . . . 5- . . . . . . . .- bl - - 4 . . . . . . ... Position (m) - - . . . . . . . .;. . . . . . . ..- -. . .- -.-;- - - -- - - --| - . . . . . . 4- - 20 - - - - --- - - . . . . .;--- - - - -- 10 Time (s) 6 (f) Draw a graph of the runner's velocity as a function of time. Note the scale listed on both axes. 20 15 Velocity (m/s) 10 5 b Time (s) 10Physics 1 Homework - Representing Motion 2 Adam, Bill, and Chad are in an airport x = 36 m A terminal and come across two moving walkways that are 36 m long. The B walkways move with a constant speed of 3m/s= 3 m/s. The three decide to have a race, -3mis but they all run at the same constant speed of 9 m/s relative to the floor. The x =0 race is as follows: At time t = 0, all three start at the same time at x = 0 and immediately reach their constant 9 m/s speed relative to the floor on which they are running. All three must run 36 m to the right, then turn around in a very short time, and run 36 m to the left back to the starting point. Adam runs his race on the non-moving floor. Bill runs his race on the walkway that moves to the right at a constant 3 m/s. Chad runs his race on the walkway that moves to the left at a constant 3 m/s. (a) Fill in each blank: During the first part, Adam's velocity relative to the Earth is number units direction During the second part, Adam's velocity relative to the Earth is number units direction During the first part, Bill's velocity relative to the Earth is number units direction During the second part, Bill's velocity relative to the Earth is number units direction During the first part, Chad's velocity relative to the Earth is number units direction During the second part, Chad's velocity relative to the Earth is number units direction (b) Draw a graph of each boy's position as a function of time for this race. Adam Bill Chad d (m) 4d (m) d (m) 36 33 30 33 27 27 24 24 21 18 21 15 18 wabNi It (s) 2 3 It (s) 10 0 2 4 5 6 7 8 9 10 0 It (s) 2 3 4 5 6 7 8 9 10AP Physics 1 Homework - Representing Motion (c) Daniel watches the race and makes the following argument: "If I take Bill's first speed and last speed and average them, I get a number that is the same as Adam's speed. If I take Chad's first speed and last speed and average them, I get the same number that is Adam's speed. Therefore, Adam, Bill, and Chad have the same average speed for this race. If all three have the same average speed and go the same distance, the race must be a tie." i. What aspects of Daniel's reasoning are correct? Explain your reasoning. ii. What aspects of Daniel's reasoning are incorrect? iii. According to your graphs, who actually wins the race? iv. In a well-organized, paragraph-length response, explain why the boy you indicated in (c)-iii wins the race even though all three boys had speeds that algebraically average to the same number. Make specific observations about distance, average speed, and time for each boy. 3. Points Given: (1) /10 (2) /15