The position vector of a particle R as a function of time t is given by 
$\overrightarrow{\mathrm{R}}=4\sin \left[2\mathrm{\pi t}\right]\hat{\mathrm{i}}+4\cos \left[2\mathrm{\pi t}\right]\hat{\mathrm{j}}$
Where R is in meters, t is in seconds and $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

1. Acceleration is along $-\overrightarrow{\mathrm{R}}$.

2. Magnitude of the acceleration vector is $\frac{{\mathrm{v}}^2}{\mathrm{R}}$, where v is the velocity of the particle.

3. Magnitude of the velocity of the particle is 8 m/s.

4. Path of the particle is a circle of radius 4m.

A particle moves in a circle of radius 5 cm with constant speed and time period $0.2\mathrm{\pi }$ sec. The acceleration of the particle is:

1.  25 m/s²

2.  36 m/s²

3.  5 m/s²

4.  15 m/s²

A particle moves in the x – y plane according to the rule x = a sin ωt and y = a cos ωt. The particle follows:

1. a circular path.

2. a parabolic path.

3. a straight line path inclined equally to x and y-axes.

4. an elliptical path.