$A$ body of mass $m$ moves with a velocity $v$ on a surface whose friction coefficient is $\mu$. If the body covers a distance $s$ before coming to rest,what is the initial velocity $v$?

The power required for an engine to maintain a constant speed of $50 \,m \,s^{-1}$ for a train of mass $3 \times 10^6 \,kg$ on rough rails is (The coefficient of kinetic friction between the rails and wheels of the train is $0.05$ and acceleration due to gravity $= 10 \,m \,s^{-2}$).

$A$ body of weight $64 \,N$ is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are $0.6$ and $0.4$ respectively, the acceleration of the body is (Acceleration due to gravity $= g$)

$A$ body is travelling with $10 \,ms^{-1}$ on a rough horizontal surface. Its velocity after $2 \,s$ is $4 \,ms^{-1}$. The coefficient of kinetic friction between the block and the plane is (acceleration due to gravity $= 10 \,ms^{-2}$)

$A$ lift is moving downwards with an acceleration equal to acceleration due to gravity. $A$ body of mass $M$ kept on the floor of the lift is pulled horizontally. If the coefficient of friction is $\mu$,what is the frictional resistance offered by the body when the lift is moving upwards with a uniform velocity?

Determine the maximum acceleration in $m/s^2$ of the train in which a box lying on its floor will remain stationary,given that the coefficient of static friction between the box and the train's floor is $0.15$.