$A$ block of mass $5\,kg$ is placed at rest on a table with a rough surface. If a force of $30\,N$ is applied parallel to the surface of the table,the block slides through a distance of $50\,m$ in $10\,s$. Calculate the coefficient of kinetic friction. (Given: $g = 10\,m/s^2$)

For the given figure,find the acceleration of the $40\, kg$ block in $m/s^2$. (Take $g = 10\, m/s^2$)

$A$ body of mass $1 \,kg$ is moving with a velocity $10 \,ms^{-1}$ on a horizontal rough surface having a coefficient of kinetic friction $0.4$. If the constant force is removed, the body comes to rest in a time (Acceleration due to gravity $g = 10 \,ms^{-2}$). (in $\,s$)

$A$ block is projected with speed $20 \,m/s$ on a rough horizontal surface. The coefficient of friction $(\mu)$ between the surfaces varies with time $(t)$ as shown in the figure. The speed of the body at the end of $4 \,s$ will be ............ $m/s$ $(g = 10 \,m/s^2)$.

$A$ particle of mass $M$ moves along a horizontal $x$-axis from $x=0$ to $x=L$. The coefficient of kinetic friction varies as a function of $x$ as $\mu(x) = \mu_0 - \alpha x$, where $\mu_0$ and $\alpha$ are constants of appropriate dimensions, such that $\mu(L)=0$. The total work done by the frictional force during the motion is $n\mu_0 MgL$, where $g$ is the acceleration due to gravity. The value of $n$ is:

$A$ movable steel plate is placed between fixed steel and brass plates and the stack of plates is subjected to a weight of $100 \ N$ as shown in the figure. The coefficient of kinetic friction for steel on steel is $0.57$ and for steel on brass is $0.44$. Assuming that the entire weight comes onto the stack and that the weight of the plates is negligible in comparison to the applied weight, the force required to move the middle plate (in $N$) is