A block of mass $m$ moving at a speed $v$ compresses a spring through a distance $x$ before its speed becomes one fourth. Find the spring constant of the spring

The position $x$ of a particle moving along $x$-axis at time $(t)$ is given by the equation $t=\sqrt{x}+2$, where $x$ is in metres and $t$ in seconds. the work done by the force in first four seconds is .............. $J$

A block of mass $1\,kg$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $8\,m/s$ , the thermal energy developed in this process .................. $\mathrm{J}$

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 $n=$

A ball is released from a height of $10\, m$. If after the impact there is loss of $40\%$ in its  energy, the ball shall rise upto- ................. $\mathrm{m}$

Which of the following graphs is correct between kinetic energy $ (E), $ potential energy $(U)$  and height $(h)$ from the ground of the particle