A particle is moving in a circle of radius R with a constant speed v. Its average acceleration over the time when it moves over half the circle is :

  1. A. \frac{v^{2}}{R}
  2. B. \frac{\pi v^{2}}{2R}
  3. C. \frac{2v^{2}}{\pi R} ✓
  4. D. 0

Correct Answer: C. \frac{2v^{2}}{\pi R}

Explanation

Average acceleration is the change in velocity divided by time. The change in velocity vector over a half-circle is 2v, and the time taken is \pi R/v. Therefore, average acceleration is 2v^2/\pi R.

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