$A$ cylinder of $10 \, kg$ is sliding on a plane with an initial velocity of $10 \, m/s$. If the coefficient of friction between the surface and the cylinder is $0.5$,then the distance it will cover before stopping is ........ $m$. $(g = 10 \, m/s^2)$

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

$A$ 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 $\left(g=10 \,m/s^2\right)$.

$A$ car accelerates on a horizontal road due to the force exerted by:

$A$ block of mass $5\, kg$ is kept on a rough horizontal floor. It is given a velocity $33\, m/s$ towards the right. $A$ force of $20\sqrt{2}\, N$ continuously acts on the block as shown in the figure. If the coefficient of friction between the block and the floor is $0.5$, the velocity of the block after $3\, seconds$ is ........ $m/s$ $(g = 10\, m/s^2)$.

$A$ block of mass $m$ rests on a rough horizontal surface as shown in the figure. The coefficient of friction between the block and the surface is $\mu$. $A$ force $F = mg$ acting at an angle $\theta$ with the vertical side of the block pulls it. In which of the following cases can the block be pulled along the surface?