A car initially traveling eastward turns north by traveling in a circular path a

Question

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 262 m, and the car completes the turn in 33.0 s.

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 262 m, and the car completes the turn in 33.0 s. What is the acceleration when the car is at B located at an angle of 35.0 degree ? Express your answer in terms of the unit vectors Determine the car's average speed. Determine its average acceleration during the 33.0-s interval.

Explanation / Answer

The length of arc is L=pi*r/2

Which is given to be 262 m

So

r=262*2/pi=166.79 m

The angular velocity of the car is w= pi/(2*33)= 0.0476 rad/s

Now, its centripetal acceleration is

aB=w^2*r=0.0476^2*166.79=0.378

So the x component is -aB*cos(35)=-0.309 m/s^2

The y component is = aB*sin(35)=0.216 m/s^2

Initial velocity is

vi=r*w i = 7.94 i m/s

Final velocity is

vf=7.94 j m/s

So the average acceleration is (Vf-Vi)/(t)= (7.94 j - 7.94 i )/33

Average acceleration x component is =-0.240 m/s^2

Average acceleration Y component is =0.240 m/s^2

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