$A$ body of mass $2 \, kg$ has an initial velocity of $3 \, m/s$ along $OE$ and it is subjected to a force of $4 \, N$ in a direction perpendicular to $OE$. The distance of the body from $O$ after $4 \, s$ will be ........... $m$.

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

$A$ projectile is launched from point $A$ of the given landscape with a water body as shown in the diagram. The launching angle is $15^{\circ}$. From the following, identify the right initial velocity of the projectile with which it will fall somewhere in between the points $C$ and $D$. [Assume $g = 10 \,m/s^2$] (in $\,m/s$)

$A$ particle is moving in a uniform circular motion with angular momentum $L$. If the frequency of motion is doubled and its kinetic energy is halved,find the new value of its angular momentum.

The position vector of a particle $\vec{R}$ as a function of time is given by $\vec{R} = 4\sin(2\pi t)\hat{i} + 4\cos(2\pi t)\hat{j}$,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 the particle?

$A$ particle is moving eastwards with a speed of $6 \, m/s$. After $6 \, s$,the particle is found to be moving with the same speed in a direction $60^{\circ}$ north of east. The magnitude of average acceleration in this interval of time is ....... $m/s^2$.