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 ABCis 214 m, and the car completes the turn in 0 s. An x y coordinate system is shown in the figure. Three points A, B, and C are shown on the graph. These points are joined by a dotted curve. Point A is on the negative y-axis, point C is on the positive x-axis, while point B is in the fourth quadrant IV at an angle of −35° with the x-axis. From point A the curve initially moves rightward along a circular path, curves upward to cross B and then meets C. An arrow indicating the velocity at point A points horizontally and to the right. An arrow indicating the velocity at point C points vertically upward. What is the acceleration when the car is at Blocated at an angle of 35.0°? Express your answer in terms of the unit vectors î and ĵ. Determine the car's average speed. Determine its average acceleration during the 34.0-s interval.

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  1. 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 ABCis 214 m, and the car completes the turn in 0 s.

An x y coordinate system is shown in the figure. Three points AB, and C are shown on the graph. These points are joined by a dotted curve. Point A is on the negative y-axis, point C is on the positive x-axis, while point B is in the fourth quadrant IV at an angle of −35° with the x-axis. From point A the curve initially moves rightward along a circular path, curves upward to cross B and then meets C. An arrow indicating the velocity at point A points horizontally and to the right. An arrow indicating the velocity at point C points vertically upward.

  1. What is the acceleration when the car is at Blocated at an angle of 35.0°? Express your answer in terms of the unit vectors î and ĵ.
  2. Determine the car's average speed.
  3. Determine its average acceleration during the 34.0-s interval.
A
35.0⁰
C
B
x
Transcribed Image Text:A 35.0⁰ C B x
Expert Solution
Introduction:

The turning of car from point A till point C is case of uniform circular motion where speed is constant. Since the direction is changing, this means that only centripital acceleration is acting on the car. We know that the magnitude of this centripital acceleration is given by

ac=v2r

where v,r are speed and radius of the circle or circular arc respectively.

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