A bullet fired into a fixed target loses $20\%$ of its kinetic energy in penetrating $1 \mathrm{cm}$. The total distance penetrated by the bullet before it comes to rest is

Find velocity of $A$ in the figure after it has started from rest at $t=0$ in the position shown and travelled $9 \mathrm{m}$ along the frictionless surface. $M_{\mathrm{A}} \& M_{\mathrm{B}}$ are $300 \mathrm{kg} \& 200 \mathrm{kg}$, respectively (take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$).

A block of mass $5 \mathrm{kg}$ is released from rest when compression in spring is $2 \mathrm{m}$. Block is not attached with the spring and natural length of the spring is $4 \mathrm{m}$. Maximum height of block from ground is$\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A power $\left(P\right)$ versus position $\left(x\right)$ graph for a particle is shown below. The particle is of mass $\frac{10}{7} \mathrm{kg}$ and is moving in a positive $x$-direction. Its initial position is $x=0$ and the initial velocity is $1 \mathrm{m} {\mathrm{s}}^{-1}$. The velocity at $x=10$ is