$A$ 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 the $OF$ direction,which is perpendicular to $OE$. The displacement of the body from $O$ after $4 \; s$ will be: (in $; m$)

The centripetal acceleration of a particle in uniform circular motion is $18 \,m/s^2$. If the radius of the circular path is $50 \,cm$, the change in velocity of the particle in a time of $\frac{\pi}{18} \,s$ is (in $\,m/s$)

$A$ particle of mass $1 \ kg$ is projected with an initial velocity $10 \ ms^{-1}$ at an angle of projection $45^{\circ}$ with the horizontal. The average torque acting on the projectile,between the time at which it is projected and the time at which it strikes the ground,about the point of projection in $Nm$ is:

$A$ sportsman runs around a circular track of radius $r$ such that he traverses the path $ABAB$. The distance travelled and displacement,respectively,are

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:

$A$ projectile is thrown with a velocity of $10\,m/s$ at an angle of $60^{\circ}$ with the horizontal. The time interval between the moments when the speed is $\sqrt{5g}\,m/s$ is $..........\,s$ (take $g=10\,m/s^2$).