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