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 meters, $t$ is 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?

1. A
   Path of the particle is a circle of radius $4$ meter
2. B
   Acceleration vector is along $-\vec{R}$
3. C
   Magnitude of acceleration vector is $\frac{v^2}{R}$, where $v$ is the velocity of particle
4. D
   Magnitude of the velocity of particle is $8$ meter/second