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# A car is traveling around a horizontal circular track with radius r = 230 m as shown. It takes the car t = 52 s to go around the track once.?

A car is traveling around a horizontal circular track with radius r = 230 m as shown. It takes the car t = 52 s to go around the track once. The angle θA = 35° above the x axis, and the angle θB = 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 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

6)

As the car passes point B, the y component of its velocity is(choose one)

increasing

constant

decreasing

### 2 Answers

- ?Lv 76 months agoFavorite Answer
1)What is the magnitude of the car’s acceleration?

angular speed ω = 2PI / T = PI / 26 rad/sec

tangential speed Vt = ω *r = 230PI/26 = 27.8 m/sec

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

Vtx = Vt*sin 35.5 = 27.8*0.581 = 16.1 m/sec

3)What is the y component Vty of the car’s velocity when it is at point A Vty = Vt*cos 35.5 = 27.8*0.814 = 22.6 m/sec

4)What is the x component ax of the car’s acceleration when it is at point B

ax = Vt^2/r*cos 59 = 27.8^2/230*0.515 = 1.73 m/sec^2

5)What is the y component ay of the car’s acceleration when it is at point B

ay = Vt^2/r*sin 59 = 27.8^2/230*0.857 = 2.88 m/sec^2

6) As the car passes point B, the y component of its velocity is(choose one)

increasing with the angle increase

- NCSLv 76 months ago
velocity v = 2πR / t = 2π*230m / 52s = 27.8 m/s

1) the car's acceleration is radial:

a = v² / R = (27.8m/s)² / 230m = 3.36 m/s²

If the car is racing counterclockwise, then

2) Vx = 27.8m/s * cos(35º+90º) = -15.9 m/s

3) Vy = 27.8m/s * sin(35º+90º) = 22.8 m/s

But if the car is racing counterclockwise, then

2) Vx = 15.9 m/s

3) Vy = -22.8 m/s

4) a_x = 3.36m/s² * cos(180º - 59º) = -1.73 m/s²

5) a_y = 3.36m/s² * sin(180º - 59º) = 2.88 m/s²

6) If the car is racing counterclockwise, then ** increasing **. But if racing counterclockwise, then ** decreasing **.

I have no doubt that your diagram shows the direction of the car.

Hope this helps!