If a body of mass $2 \,kg$ moving with an initial velocity of $4 \,m \,s^{-1}$ is subjected to a force of $3 \,N$ for a time of $2 \,s$ normal to the direction of its initial velocity, then the resultant velocity of the body is

$A$ person sitting in an open car moving at a constant velocity throws a ball vertically up into the air. The ball falls:

Two stones of masses $m$ and $2\,m$ are whirled in horizontal circles,the heavier one in a radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is

The position vector of a particle moving in a plane is given by $r = a \cos \omega t \hat{i} + b \sin \omega t \hat{j}$, where $\hat{i}$ and $\hat{j}$ are the unit vectors along the rectangular axes $X$ and $Y$; $a$, $b$, and $\omega$ are constants, and $t$ is time. The acceleration of the particle is directed along the vector:

$A$ person walks in such a way that he covers equal distance in each step. The person takes $2$ steps forward towards East, then takes a right turn and walks $4$ steps towards South, then takes a right turn and walks $6$ steps towards West, and then takes a right turn and walks further. The direction of his final position after a total of $20$ steps walk with respect to his initial position is:

$A$ particle moves towards east with velocity $5\, m/s$. After $10\, s$,its direction changes towards north with the same velocity. The average acceleration of the particle is