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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^2

Explanation / 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/s2