question_answer

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?

A)  Path of the particle is a circle of radius 4 meter

B)  Acceleration vectors is along \[-\vec{R}\]

C)  Magnitude of acceleration vector is \[\frac{{{v}^{2}}}{R}\] where v is the velocity of particle.

D)  Magnitude of the velocity of particle is 8 meter/second