The position vector of a particle $\vec R$ as a function of time is given by $\overrightarrow {\;R} = 4\sin \left( {2\pi t} \right)\hat i + 4\cos \left( {2\pi t} \right)\hat j$ 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 particle starts from the origin at $t=0$ $s$ with a velocity of $10.0 \hat{ j } \;m / s$ and moves in the $x-y$ plane with a constant acceleration of $(8.0 \hat{ i }+2.0 \hat{ j }) \;m \,s ^{-2} .$

$(a)$ At what time is the $x$ – coordinate of the particle $16\; m ?$ What is the $y$ -coordinate of the particle at that time?

$(b)$ What is the speed of the particle at the time?

A particle starts from origin at $t=0$ with a velocity $5.0 \hat{ i }\; m / s$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3.0 \hat{ i }+2.0 \hat{ j })\; m / s ^{2} .$

$(a)$ What is the $y$ -coordinate of the particle at the instant its $x$ -coordinate is $84 \;m$ ?

$(b)$ What is the speed of the particle at this time?