$A$ fireman of mass $60 \ kg$ slides down a pole. He is pressing the pole with a force of $600 \ N$. The coefficient of friction between the hands and the pole is $0.5$. With what acceleration (in $m/s^2$) will the fireman slide down? (Take $g = 10 \ m/s^2$)

The coefficient of friction between the block of mass ${M_1}$ and the surface is $\mu$. When the system is released,it moves with acceleration. What mass $m$ should be placed on the block ${M_1}$ so that the system moves with a constant velocity?

When the engine is switched off, a vehicle of mass $M$ is moving on a rough horizontal road with momentum $p$. If the coefficient of friction between the road and the tyres of the vehicle is $\mu_k$, what is the distance travelled by the vehicle before it comes to rest?

$A$ block of $7\,kg$ is placed on a rough horizontal surface and is pulled by a variable force $F$ (in $N$) $= 5t$,where $t$ is time in seconds,at an angle of $37^{\circ}$ with the horizontal as shown in the figure. The coefficient of static friction between the block and the surface is $\mu = 1$. If the force starts acting at $t = 0\,s$,find the time at which the block starts to slide. (Take $g = 10\,m/s^2$)

$A$ block of a certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are $0.4$ and $0.25$ respectively. $A$ constant horizontal force $F = 20 \text{ N}$ acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take $g = 10 \text{ m/s}^2$): (in $\text{ kg}$)

$A$ 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 $\,s$)