Under the action of a force, a $2 \,kg$ body moves such that its position $x$ as a function of time $t$ is given by $x=\frac{t^2}{3}$, where $x$ is in metres and $t$ in seconds. The workdone by the force in first two seconds is .......... $J$

A body of mass ' ${m}$ ' dropped from a height ' ${h}$ ' reaches the ground with a speed of $0.8 \sqrt{{gh}}$. The value of workdone by the air-friction is $.....\,{mgh}$

A ball is thrown vertically downwards from a height of  $20\, m$ with an initial velocity $v_0$, It collides with the ground, loses $50$ percent of its energy in collision and rebounds same height. The initial velocity $v_0$ .................... $\mathrm{ms}^{-2}$ (Take $g=10 \,ms^{-2}$)

A bullet of mass $20\,g$ has an initial speed of $1\,ms^{-1}$ just before it starts penetrating a mud wall of thickness $20\,cm.$ If the wall offers a mean resistances of $2.5 \times 10^{-2}\,N,$ the speed of the bullet after emerging from the other side of the wall is close to .............. $\mathrm{ms}^{-1}$

A ball is dropped from a height of $20\, cm$. Ball rebounds to a height of $10\, cm$. What is the loss of energy ? ................ $\%$

Consider an elliptically shaped rail $P Q$ in the vertical plane with $O P=3 \ m$ and $OQ =4 \ m$. A block of mass $1 \ kg$ is pulled along the rail from $P$ to $Q$ with a force of $18 \ N$, Which is always parallel to line $PQ$ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches $Q$ is $(n \times 10)$ joules. The value of $n$ is (take acceleration due to gravity $=10 \ ms ^{-2}$ )