$A$ bag is gently dropped on a conveyor belt moving at a speed of $2\,m/s$. The coefficient of friction between the conveyor belt and the bag is $0.4$. Initially,the bag slips on the belt before it stops slipping due to friction. The distance travelled by the bag on the belt during the slipping motion is $.....m$. [Take $g=10\,m/s^{-2}$]

When two surfaces are coated with a lubricant,then they

$A$ block of mass $5\, kg$ is kept on a rough horizontal floor. It is given a velocity $33\, m/s$ towards the right. $A$ force of $20\sqrt{2}\, N$ continuously acts on the block as shown in the figure. If the coefficient of friction between the block and the floor is $0.5$, the velocity of the block after $3\, seconds$ is ........ $m/s$ $(g = 10\, m/s^2)$.

$A$ block of mass $m$ (initially at rest) is sliding up a rough vertical wall with the help of a force $F$ whose magnitude is constant but direction is changing. $\theta = {\theta _0}t$,where $t$ is time in seconds. At $t = 0$,the force is in the vertical upward direction,and as time passes,its direction changes until $\theta = \frac{\pi }{2}$. The value of $F$ such that the block comes to rest when $\theta = \frac{\pi }{2}$ is:

$A$ cylinder of mass $12 \,kg$ is sliding on a plane with an initial velocity $20 \,ms^{-1}$. If the coefficient of friction between the surface and the cylinder is $0.5$, what is the distance the cylinder travels before stopping (in $\,m$)?

$A$ block of mass $100 \ kg$ slides over a distance of $10 \ m$ on a horizontal surface. If the coefficient of friction between the surfaces is $0.4$,then the work done against friction (in $J$) is: