The position vector of a moving particle at time $t$ is $r =3 \hat{ i }+4 t \hat{ j }-t \hat{ k }$. Its displacement during the time interval $t=1 s$ to $t=3 s$ is

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? 

Give examples of one dimensional, two dimensional and three dimensional motion.

A hiker stands on the edge of a cliff $490\; m$ above the ground and throws a stone horizontally with an initial speed of $15 \;m/ s$. Neglecting air resistance, find the time taken by the stone to reach the ground, and the speed with which it hits the ground. (Take $g = 9.8 \;m /s^2$ ).

A particle moves in $x-y$ plane with velocity $\vec v = a\widehat i\, + \,bx\widehat j$ where $a$ & $b$ are constants. Initially particle was at origin then trajectory equation is:-

At time $t =0$ a particle starts travelling from a height $7\,\hat{z} cm$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $x$ and $y$ directions are defined as $3\,t$ and $5\,t^{3}$ respectively. At $t =1\,s$ acceleration of the particle will be.