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

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zwbbql132

Science

Question Description

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure. The length of the arc ABC is 270 m, and the car completes the turn in 31.0 s.

(a) Determine the car's speed.
 m/s

(b) What is the magnitude and direction of the acceleration when the car is at point B?
magnitude      m/s2
direction  ° counterclockwise from the +x-axis 

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Explanation & Answer

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The length of the arc is for a 90 degree or (π/2) radians is 
l = rθ 
l = 270*(π/2) 
l = 424.1 m 

so the constant speed is 
v = l/t 
v = 424.1 / 31 
v = 13.68 m/s 

acceleration at a uniform speed on a circular curve is 
a = v²/r 
a = 13.68² / 270 
a = 0.693 m/s² 

and the direction will be towards the center of the curve which will be perpendicular to the instantaneous velocity. 
35° + 90° = 125°

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Sngva Zraunm (1755)
Boston College

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