Acar is traveling around a horizontal circular track with radius r = 220 m as shown. it takes the car t = 61 s to go around the track once. the angle θa = 23° above the x axis, and the angle θb = 57° below the x axis.
1) what is the magnitude of the car’s acceleration?
2) what is the x component of the car’s velocity when it is at point a
3) what is the y component of the car’s velocity when it is at point a
4) what is the x component of the car’s acceleration when it is at point b
5) what is the y component of the car’s acceleration when it is at point b

Refer to the diagram shown below.

Because the time to go around the track is 61 s, the angular velocity is
ω = (2π rad)/(61 s) = 0.103 rad/s
The tangential velocity is
v = rω = (220 m)*(0.103 rad/s) = 22.66 m/s

Part 1)
The centripetal acceleration is
a = v²/r = (22.66 m/s)²/(220 m) = 2.334 m/s²
The centripetal acceleration is directed toward the center of the circle.

2.334 m/s²

Part B)

The x-component of the velocity at A is
- v*sin(23°) = -22.66*sin(23°) = - 8.854 m/s

- 8.854 m/s

Part 3)
The y-component of the velocity at A is
v* cos(23°) = 22.66*cos(23°) = 20.86 m/s

20.86 m/s

Part 4)
The x-component of the acceleration at B is
- a*cos(57°) = - (2.334 m/s²)*cos(57°) =  -1.27 m/s²

- 1.27 m/s²

Part 5)
The y-component of acceleration at B is
a*sin(57°) = (2.334 m/s²)*sin(57°) = 1.96 m/s²

1.96 m/s²

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.