The position vector of a particle R→ as a function

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The position vector of a particle R^{^→} as a function of time is given by :
R^{^→} = 4sin(2πt)î + 4cos(2πt)ĵ
Where R is in meter, t in seconds and î and ĵ denote unit vectors along x-and y-directions, respectively.
Which one of the following statements is wrong for the motion of particle?

1. Magnitude of acceleration vector is v² , where v is the velocity of particle
  R
2. Magnitude of the velocity of particle is 8 meter/second
3. path of the particle is a circle of radius 4 meter.
4. Acceleration vector is along R^{^→}

Correct Option: B

Here,x = 4sin(2πt)...(i)
y = 4cos(2πt)...(ii)
Squaring and adding equation (i) and (ii)
x² + y² = 4² ⇒ R = 4
Motion of the particle is circular motion, accelerationvector is along – R^{^→} and its magnitude

=	V²
	R

Velocity of particle, V = ωR = (2π) (4) = 8π

Magnitude of acceleration vector is	v²	, where v is the velocity of particle
	R