The position vector of a particle is R = 4 sin(2πt)i + 4 cos(2πt)j, where R is in metres and t is in seconds. Which statement is WRONG?
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Question

The position vector of a particle is R = 4 sin(2πt)i + 4 cos(2πt)j, where R is in metres and t is in seconds. Which statement is WRONG?

G1 Physics · Accepted Answer

Step 1: x²+y²=16, so the path is a circle of radius 4 m. Step 2: Differentiate to get v = 8π cos(2πt)i - 8π sin(2πt)j, so speed is 8π m s⁻¹, not 8 m s⁻¹. Step 3: The acceleration is centripetal, equal to -(2π)²R and has magnitude v²/R. Therefore statement C is wrong. Final answer: C.