The positions vector of a particle $\overrightarrow R $ as a function of time is given by $\overrightarrow R $ = 4sin(2$\pi $t)$\widehat i$ + 4cos(2$\pi $t)$\widehat j$. Where R is in meters, t is in seconds and $\widehat i$ and $\widehat j$ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

Question

Magnitude of the velocity of particle is 8 meter/second.

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

Acceleration vector is along $-$$\overrightarrow R $.

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

Solution

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