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Suppose you are driving a car in a counterclockwise direction on a circular road whose radius is r = 390 m (see the figure). 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 = 32 m/s) along a circular path have an acceleration? (ii) Is there a tangential acceleration T when the angular speed of an object changes (e.g., when the car s angular speed decreases to 4.9 × 10-2 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 × 10-2 rad/s in a time of 4.0 s. What is the tangential acceleration (magnitude and direction) of the car? |
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