$A$ vehicle of mass $M$ is moving with momentum $P$ on a rough horizontal road. The coefficient of friction between the tyres and the horizontal road is $\mu$. The stopping distance is ($g$ $=$ acceleration due to gravity).

$A$ 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:

$A$ 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?

What is kinetic friction? What is rolling friction?

$A$ 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

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 $0.15$.