$A$ conveyor belt is moving at a constant speed of $2\, ms^{-1}$. $A$ box is gently dropped on it. The coefficient of friction between them is $\mu = 0.5$. The distance that the box will move relative to the belt before coming to rest on it,(taking $g = 10\, ms^{-2}$) is ........ $m$.

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 $0.15$.

$A$ body of mass $20 \,kg$ is moving on a rough horizontal plane. $A$ block of mass $3 \,kg$ is connected to the $20 \,kg$ mass by a string of negligible mass through a smooth pulley as shown in the figure. The tension in the string is $27 \,N$. The coefficient of kinetic friction between the heavier mass and the surface is $\left(g=10 \,m/s^2\right)$.

$A$ block is projected with speed $20 \,m/s$ on a rough horizontal surface. The coefficient of friction $(\mu)$ between the surfaces varies with time $(t)$ as shown in the figure. The speed of the body at the end of $4 \,s$ will be ............ $m/s$ $(g = 10 \,m/s^2)$.

$A$ vehicle of mass $m$ is moving on a rough horizontal road with momentum $P$. If the coefficient of friction between the tyres and the road is $\mu$,then the stopping distance is:

$A$ block of mass $m$ is moving on a rough horizontal surface. The coefficient of kinetic friction between the block and the surface is $\mu_{k}$. The net force exerted by the surface on the block is (where $g$ is the acceleration due to gravity).