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 figure. The speed of body at the end of $4$ second will be ............ $m / s$ ( $g=$ $10 \,m / s ^2$ )

$STATEMENT-1$ It is easier to pull a heavy object than to push it on a level ground. and

$STATEMENT-2$ The magnitude of frictional force depends on the nature of the two surfaces in contact.

A sphere of mass $m$ is set in motion with initial velocity $v_o$ on a surface on which $kx^n$ is the frictional force with $k$ and $n$ as the constants and $x$ as the distance from the point of start. Find the distance in which sphere will stop

A block of weight $W$ rests on a horizontal floor with coefficient of static friction $\mu .$ It is desired to make the block move by applying minimum amount of force. The angle $\theta $ from the horizontal at which the force should be applied and magnitude of the force $F$ are respectively.

A bullet of mass $0.1\,kg$ moving horizontally with speed $400\,ms ^{-1}$ hits a wooden block of mass $3.9\,kg$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20\,m$ before coming to rest. The coefficient of friction between the block and the surface is $........$ $\left(\text { Given } g=10 \,ms ^2\right. \text { ) }$

A block slides down on incline of angle $30^o$ with an acceleration $\frac{g}{4}$. Find the coefficient of kinetic friction