$A$ body of mass $5 \,kg$ is thrown vertically up with a kinetic energy of $490 \,J$. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity $=9.8 \,ms^{-2}$) (in $\,m$)

$A$ child is swinging on a swing. The minimum and maximum heights of the swing from the earth's surface are $0.75\,m$ and $2\,m$ respectively. The maximum velocity of this swing is ............. $m/s$.

$A$ particle of mass $m \ kg$ moves along the $X$-axis with its velocity varying with the distance travelled as $v=k x^\beta$, where $k$ is a positive constant. The total work done by all the forces during displacement of the particle from $x=0$ to $x=d$ is close to

$A$ particle is placed at the point $A$ of a frictionless track $ABC$ as shown in the figure. It is gently pushed toward the right. The speed of the particle when it reaches the point $B$ is: (Take $g = 10 \ m/s^2$).

$A$ block of mass $\sqrt{2} \, kg$ is released from the top of an inclined smooth surface as shown in the figure. If the spring constant of the spring is $100 \, N/m$ and the block comes to rest after compressing the spring by $1 \, m$,then the total distance travelled by the block along the incline before it comes to rest is ......... $m$.

$A$ bullet of mass $25\,g$ moving with a velocity of $200\,m/s$ is stopped within $5\,cm$ of the target. The average resistance offered by the target is ............... $kN$.