$A$ ring of mass $m$ moves from point $1$ to point $2$ along a smooth rigid horizontal wire with a constant speed $v$. The average force acting on the ring over the time of its motion from $1$ to $2$ is

$A$ 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 $; m$)

$A$ ball is dropped from a height of $49\,m$. The wind is blowing horizontally. Due to wind,a constant horizontal acceleration is provided to the ball. Choose the correct statement$(s)$. (Take $g = 9.8\,m/s^2$)

$A$ car goes around a uniform circular track of radius $R$ at a uniform speed $v$ once in every $T$ seconds. The magnitude of the centripetal acceleration is $a_c$. If the car now goes uniformly around a larger circular track of radius $2R$ and experiences a centripetal acceleration of magnitude $8a_c$,then its time period is:

The greatest height to which a man can throw a stone is $h$. The greatest distance to which he can throw it will be:

At any time $t$,the coordinates of a moving particle are $x = at^2$ and $y = bt^2$. The speed of the particle is