A car is traveling around a horizontal circular track with radius r = 210 m as s

Question

A car is traveling around a horizontal circular track with radius r = 210 m as shown. It takes the car t = 50 s to go around the track once. The angle A = 29° above the x axis, and the angle B = 65° 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

Explanation / Answer

The car posess centripetal acceleration., Centripetal acceleration, a = v^2 / r

here V = 2piR/T

V = 2*3.14* 210/50

V = 26.376 m/s

1. Centripetal acceleration, a = V^2/R

a = 26.376*26.376 /210

a = 3.312 m/s^2
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x component of velocity Vx = V cos theta

Vx = 26.376 * cos 29

Vx = 23.06 m/s

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Y -component of velocity

Vy = V cos 65

Vy = 26.375 * cos 65

Vy = 2.5 * cos 35

Vy = 11.14 m/s

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x-component of acceleration, a x= a cos theta

Ax = 3.312 * cos 35

Ax = 2.713 m/s^2

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y components of accleratio n

Ay = A sin theta

Ay = 3.312 * sin 65

Ay = 3 m/s^2

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