A car is traveling around a horizontal circular track with radius r = 240 m at a

Question

A car is traveling around a horizontal circular track with radius r = 240 m at a constant speed v = 25 m/s as shown. The angle A = 29° above the x axis, and the angle B = 59° below the x axis.

1)What is the magnitude of the car’s acceleration?

2) What is the x component of the car’s acceleration when it is at point A

3) What is the y component of the car’s acceleration 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

6) As the car passes point B, the y component of its acceleration is

a) increasing

b) constant

c) decreasing

Explanation / Answer

Unfortunately not see the figure, the problem would be clearer. I'll answer it as I understand it your text

Part 1)

The expression for centripetal acceleration is

ac = V2 /R

ac = 252 /240

ac = 2.60 m/s2

Part 2)

We found the velocity components using trigonometry

Cos = Vx/V

Sin = Vy/V

Vx = V Cos

Vx = 25 Cos 29

Vx = 21.87 m/s

Part 3)

Vy = 25 Sin 29

Vy = 12.12 m/s

Part 4)

In this case the angle is measured clockwise

= -59

or counterclockwise

= 360 -59 = 301

Vx = 25 Cos (-59)

Vx = 12.88 m/s

Part 5)

Vy = 25 Sin (-59) = 25 Sin (301)

Vy = - 21.43 m/s

Part 6)

The centripetal acceleration does not change with angle

ac = V2 /R

ac = 2.60 m/s2

But each component of the acceleration may change

ac = sqrt( ax2 + ay2 )

I think your question refers to the change in acceleration between points A and B

(Vy )A = 12.12 m/s

(Vy)B = -21.43 m/s

ay= (Vf-Vo)/t =((Vy)B - (Vy)A ) / t

ay = (-21.43 – 12.12 )/t

ay = 33.55 / t

Consequently acceleration on the axis and is directed in the opposite direction of motion and increases to change the speed value from positive to negative

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