Suppose you are driving a car in a counterclockwise

Chapter , Problem 79

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Suppose you are driving a car in a counterclockwise direction on a circular road whose radius is r 5 390 m (see the fi gure). You look at the speedometer and it reads a steady 32 m/s (about 72 mi/h). Concepts: (i) Does an object traveling at a constant tangential speed (for example, vT 5 32 m/s) along a circular path have an acceleration? (ii) Is there a tangential acceleration aT B when the angular speed of an object changes (e.g., when the cars angular speed decreases to 4.9 3 1022 rad/s)? Calculations: (a) What is the angular speed of the car? (b) Determine the acceleration (magnitude and direction) of the car. (c) To avoid a rear-end collision with the vehicle ahead, you apply the brakes and reduce your angular speed to 4.9 3 1022 rad/s in a time of 4.0 s. What is the tangential acceleration (magnitude and direction) of the car?