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A car travels around a circular curve of radius 10 m at a constant speed of 10 m/s. Consider the portion of the motion during which the car sweeps out a 120 deg arc. Which of the following statements is correct?

1. The magnitude of the resultant change in velocity of the car is 10*sqrt(3) m/s
2. The instantaneous acceleration of the car is 10 m/s²
3. The average acceleration of the car is 5/24 m/s²
4. The instantaneous and average accelerations are equal for this part of the motion

Correct answer: The instantaneous acceleration of the car is 10 m/s²

Solution

Instantaneous acceleration = v²/r = 100/10 = 10 m/s², which is correct. The change in velocity over 120 deg is 2v sin60 = 10*sqrt(3) m/s but that is |dv| not the average value, and average acceleration differs from instantaneous.

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