$A$ uniform rope of total length $l$ is at rest on a table with a fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the rope is $\mu$,then:

$A$ 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 $m$ placed on a rough horizontal plane is pulled by a constant power $P$. The coefficient of friction between the block and the surface is $\mu$. The maximum velocity of the block will be

$A$ block of mass $10\, kg$ moving at $10\, m/s$ is released to slide on a rough surface having a coefficient of friction $0.2$. It will stop after travelling a distance of ........ $m$.

$A$ car is moving along a straight horizontal road with a speed $v_0$. If the coefficient of friction between the tyres and the road is $\mu$,the shortest distance in which the car can be stopped is

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