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The position vector of a particle $\vec{R}$ as a function of time is given by: $\vec{R} = 4 \sin (2\pi t)\hat{i} + 4 \cos (2\pi t)\hat{j}$,Where R is in meter, t in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
Explanation
Here, $x = 4 \sin(2\pi t)$, $y = 4 \cos(2\pi t)$ Squaring and adding equations (i) and (ii) $x^{2} + y^{2} = 4^{2} \Rightarrow R = 4$ Motion of the particle is circular motion, acceleration vector is along $-\vec{R}$ and its magnitude = $V^{2}/R$ Velocity of particle, $V = \omega R = (2\pi)(4) = 8\pi$