$A$ particle of mass '$m$' at rest on a rough horizontal surface with a coefficient of friction '$\mu$' is given a velocity '$u$'. The average power imparted by friction before it stops is:

$A$ 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 $g = 10\,m/s^2$)

$A$ boat of mass $700 \,kg$ is travelling at a speed of $24 \,ms^{-1}$ when its engine is shut off. The magnitude of frictional force $f$ between the boat and water is given by $f = 35v$, where $v$ is the speed in $ms^{-1}$ and $f$ is in newton. Find the time taken for the speed of the boat to become $6 \,ms^{-1}$. (in $\,s$)

$A$ block of mass $40 \,kg$ slides over a surface,when a mass of $4 \,kg$ is suspended through an inextensible massless string passing over a frictionless pulley as shown below. The coefficient of kinetic friction between the surface and the block is $0.02$. The acceleration of the block is ............ $m/s^2$. (Given $g = 10 \,m/s^2$.)

If the normal reaction is $R$ and the coefficient of friction is $\mu$,what is the work done against friction in moving a body by a distance $d$ slowly?

$A$ $2 \, kg$ block on ice is given a velocity of $6 \, m/s$. If it comes to rest in $10 \, s$,what is the coefficient of friction?