A body of mass $1\, kg$ is under a force, which causes a displacement in it is given by $x = \frac{{{t^3}}}{3}$ (in $m$). Find the work done by the force in first second ............ $\mathrm{J}$

A cricket ball of mass $0.15\, kg$ is thrown vertically up by a bowling machine so that it rises to a maximum height of $20 \;m$ after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves horizontally a distance of $0.2\, m$ while launching the ball, the value of $F($ in $N)$ is 

$\left(g=10\, m s^{-2}\right)$

A block of mass ' $m$ ' (as shown in figure) moving with kinetic energy $E$ compresses a spring through a distance $25\,cm$ when, its speed is halved. The value of spring constant of used spring will be $nE\; Nm ^{-1}$ for $n=$

Two inclined planes are placed as shown in figure.

A block is projected from the Point $A$ of inclined plane $A B$ along its surface with a velocity just sufficient to carry it to the top Point $B$ at a height $10 m$. After reaching the Point $B$ the block slides down on inclined plane $BC$. Time it takes to reach to the point $C$ from point $A$ is $t (\sqrt{2}+1) s$. The value of $t$ is........(use $g =10 m / s ^{2}$ )

A bullet of mass $20 \,g$ leaves a riffle at an initial speed $100 \,m / s$ and strikes a target at the same level with speed $50 \,m / s$. The amount of work done by the resistance of air will be ......... $J$

A force acts on a $3 \,gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4{t^2} + {t^3}$, where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,seconds$ is ..... $mJ$