v x avg=? m/s An athlete starts at point A and runs at a constant speed of 6.60
ID: 1958620 • Letter: V
Question
v x avg=? m/s
An athlete starts at point A and runs at a constant speed of 6.60 m/s around a round track 100 m in diameter, as shown in figure. Part A) Find the x component of this runner^'s average velocity between points A and B. v x avg=? m/s Part B) Find the y component of this runner^'s average velocity between points A and B. v y avg=? m/s Part C) Find the x component of this runner^'s average acceleration between points A and B. a x avg? m/s^2 Part D) Find the y component of this runner^'s average acceleration between points A and B. a y avg? m/s^2Explanation / Answer
The speed of an athlete, v = 6.60 m/s The diameter of the circular path of the runner, D = 100 m The radius of the circular path of the runner, r = D/2 = (100 m)/2 = 50 m ________________________________________________________________ The distance traveled by an athlete in one complete revolution is d = 2r = (2)(50 m) = 314 m The time of travel for one complete rotation is t = d/v = (314 m)/(6.60 m/s) = 47.5757 s __________________________________________________________________ The time taken to travel from poian A to B is given by tAB = t/4 = (47.5757 s)/4 = 11.894 s ___________________________________________________________________ The displacement from A to B, x = r2+r2 = (2)r = (2)(50 m) = 70.71 m ___________________________________________________________________ a) From point A to B, the x-component of the speed of an athlete is changes from zero to 6.60 m/s. From point A to B, the y-component of the speed of an athlete is changes from 6.60 m/s to zero. The x-component of the average velocity of the runner from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,av)AB = (vy,av)AB The average velocity of the runner from point A to B is vavg = [(vx,av)AB]2+[(vy,av)AB]2 = 2[(vx,av)AB]2 = (2)[(vx,avg)AB] ...... (1) __________________________________________________________________ The average velocity of the runner from point A to B is vav = x/tAB = (70.71 m)/(11.894 s) = 5.945 m/s This value substitute in equation (1), we get 5.945 m/s = (2)[(vx,av)AB] Then, the x component of this runner's average velocity between points A and B is (vx,avg)AB= 4.20 m/s __________________________________________________________________ __________________________________________________________________ b) The x-component of the average velocity of the runner from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,avg)AB = (vy,avg)AB Then, the y component of this runner's average velocity between points A and B is (vy,avg)AB= 4.20 m/s ___________________________________________________________________ ___________________________________________________________________ c) The x-component of the average acceleration between point A and B is ax,avg = [vy,AB - vx,AB]/tAB = [6.60 m/s - 0 m/s]/(11.894 s) = 0.55 m/s2 ____________________________________________________________________ d) At point A, vx,AB = 6.60 m/s At point B, vy,AB = 0 m/s The y-component of the average acceleration between point A and B is ay,avg = [vy,AB - vx,AB]/tAB = [0 m/s - 6.60 m/s]/(11.894 s) = -0.55 m/s2 = (2)(50 m) = 314 m The time of travel for one complete rotation is t = d/v = (314 m)/(6.60 m/s) = 47.5757 s __________________________________________________________________ The time taken to travel from poian A to B is given by tAB = t/4 = (47.5757 s)/4 = 11.894 s ___________________________________________________________________ The displacement from A to B, x = r2+r2 = (2)r = (2)(50 m) = 70.71 m ___________________________________________________________________ a) From point A to B, the x-component of the speed of an athlete is changes from zero to 6.60 m/s. From point A to B, the y-component of the speed of an athlete is changes from 6.60 m/s to zero. The x-component of the average velocity of the runner from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,av)AB = (vy,av)AB The average velocity of the runner from point A to B is vavg = [(vx,av)AB]2+[(vy,av)AB]2 = 2[(vx,av)AB]2 = (2)[(vx,avg)AB] ...... (1) __________________________________________________________________ The average velocity of the runner from point A to B is vav = x/tAB = (70.71 m)/(11.894 s) = 5.945 m/s This value substitute in equation (1), we get 5.945 m/s = (2)[(vx,av)AB] Then, the x component of this runner's average velocity between points A and B is (vx,avg)AB= 4.20 m/s __________________________________________________________________ __________________________________________________________________ b) The x-component of the average velocity of the runner from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,avg)AB = (vy,avg)AB Then, the y component of this runner's average velocity between points A and B is (vy,avg)AB= 4.20 m/s The displacement from A to B, x = r2+r2 = (2)r = (2)(50 m) = 70.71 m = (2)(50 m) = 70.71 m ___________________________________________________________________ a) From point A to B, the x-component of the speed of an athlete is changes from zero to 6.60 m/s. From point A to B, the y-component of the speed of an athlete is changes from 6.60 m/s to zero. The x-component of the average velocity of the runner from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,av)AB = (vy,av)AB The average velocity of the runner from point A to B is vavg = [(vx,av)AB]2+[(vy,av)AB]2 = 2[(vx,av)AB]2 = (2)[(vx,avg)AB] ...... (1) __________________________________________________________________ The average velocity of the runner from point A to B is vav = x/tAB = (70.71 m)/(11.894 s) = 5.945 m/s This value substitute in equation (1), we get 5.945 m/s = (2)[(vx,av)AB] Then, the x component of this runner's average velocity between points A and B is (vx,avg)AB= 4.20 m/s __________________________________________________________________ __________________________________________________________________ b) The x-component of the average velocity of the runner from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,avg)AB = (vy,avg)AB Then, the y component of this runner's average velocity between points A and B is (vy,avg)AB= 4.20 m/s an athlete is changes from zero to 6.60 m/s. From point A to B, the y-component of the speed of an athlete is changes from 6.60 m/s to zero. The x-component of the average velocity of the runner from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,av)AB = (vy,av)AB The average velocity of the runner from point A to B is vavg = [(vx,av)AB]2+[(vy,av)AB]2 = 2[(vx,av)AB]2 = (2)[(vx,avg)AB] ...... (1) __________________________________________________________________ __________________________________________________________________ The average velocity of the runner from point A to B is vav = x/tAB = (70.71 m)/(11.894 s) = 5.945 m/s This value substitute in equation (1), we get 5.945 m/s = (2)[(vx,av)AB] Then, the x component of this runner's average velocity between points A and B is (vx,avg)AB= 4.20 m/s __________________________________________________________________ __________________________________________________________________ b) The x-component of the average velocity of the runner from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,avg)AB = (vy,avg)AB from A to B is equal to the y-component of the average velocity of the runner from A to B. (vx,avg)AB = (vy,avg)AB Then, the y component of this runner's average velocity between points A and B is (vy,avg)AB= 4.20 m/s ___________________________________________________________________ ___________________________________________________________________ c) The x-component of the average acceleration between point A and B is ax,avg = [vy,AB - vx,AB]/tAB = [6.60 m/s - 0 m/s]/(11.894 s) = 0.55 m/s2 ____________________________________________________________________ d) At point A, vx,AB = 6.60 m/s At point B, vy,AB = 0 m/s The y-component of the average acceleration between point A and B is ay,avg = [vy,AB - vx,AB]/tAB = [0 m/s - 6.60 m/s]/(11.894 s) = -0.55 m/s2 = [6.60 m/s - 0 m/s]/(11.894 s) = 0.55 m/s2 ____________________________________________________________________ d) At point A, vx,AB = 6.60 m/s At point B, vy,AB = 0 m/s The y-component of the average acceleration between point A and B is ay,avg = [vy,AB - vx,AB]/tAB = [0 m/s - 6.60 m/s]/(11.894 s) = -0.55 m/s2 ____________________________________________________________________ d) At point A, vx,AB = 6.60 m/s At point B, vy,AB = 0 m/s The y-component of the average acceleration between point A and B is ay,avg = [vy,AB - vx,AB]/tAB = [0 m/s - 6.60 m/s]/(11.894 s) = -0.55 m/s2 ay,avg = [vy,AB - vx,AB]/tAB = [0 m/s - 6.60 m/s]/(11.894 s) = -0.55 m/s2 = [0 m/s - 6.60 m/s]/(11.894 s) = -0.55 m/s2Related Questions
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