### 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.

m/s

(b) What is the magnitude and direction of the acceleration when the car is at point

*B*?

magnitude | m/s^{2} |

direction | ° counterclockwise from the +x-axis |

## 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°