The position vector of a particle `vec(R )` as a funtion of time is given by:
`vec(R )= 4sin(2pit)hat(i)+4cos(2pit)hat(j)`
Where `R` is in meters, `t` is in seconds and `hat(i)` and `hat(j)` denote until vectors along x-and y- directions, respectively Which one of the following statements is wrong for the motion of particle ?

Options

A. Magnitude of acceleration vector is `v^(2)/R`, where v is the velocity of particle
B. Magnitude of the velocity of particle is `8pi m//s`
C. Path of the particle is a circle of radius 4m
D. Acceleration vector is along - `vecR`

Answer

B

Explanation

`x = 4 sin(2pit), y = 4 cos (2pit)`
Squarring and adding, `x^(2) + y^(2) = 4^(2) rArr R =4`
`rArr` Circular motion, `V = omegaR = (2pi)(4) = 8pi`