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 269 m, and the car completes the turn in 42.0s 01 35.0° (a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors i andj m/s i+ m/s2 (b) Determine the car's average speed. m/s (c) Determine its average acceleration during the 42.0-s interval. m/s2 i+ m/s2j Need Help?Read ItWatch I

Explanation / Answer

length of arc s = (2*pi*r)/4 = 269

radius r = 171.25 m

speed of car v = s/t = 269/42 = 6.4 m/s

(a)

radial accelration a tpoint B a_rad = v^2/r = 6.4^2/171.25 = 0.24 m/s^2

radial acceleration is directed towards the center

a = -a_rad*cos35 i + a_rad*sin35 j

a = 0.24*cos35 i + 0.24*sin35 j

a = -0.2 i + 0.14 j

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(b)

average speed v = s/t = 6.4 m/s

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(c)

average acceleration a_avg = (vc - VA)/t

VC = 6.4 j

VA = 6.4 i

a_avg = (6.4j - 6.4 i)/42

a_avg = -0.15 i + 0.15 j

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