A ball is dropped from a height and falls due to gravity and wind simultaneously imparts it a uniform horizontal acceleration. Which one of the following figures best represents its path?

Give explanation of position and displacement vectors for particle moving in a plane by giving suitable equations.

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? 

If a particle takes $t$ second less and acquires a velocity of $v \ ms^{^{-1}}$ more in falling through the same distance (starting from rest) on two planets where the accelerations due to gravity are $2 \,\, g$ and $8 \,\,g$ respectively then $v=$

A point moves in $x-y$ plane as per $x=kt,$ $y = kt\left( {1 - \alpha t} \right)$ where $k\,\& \,\alpha \,$ are $+ve$ constants. The equation of trajectory is 

“Explain average acceleration and instantaneous acceleration.”