$A$ 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 $= 10 \,ms^{-2}$)

An object of mass $1 \,kg$ moving on a horizontal surface with initial velocity $8 \,m/s$ comes to rest after $10 \,s$. If one wants to keep the object moving on the same surface with velocity $8 \,m/s$,the force required is ...... $N$.

$A$ car having a mass of $1000\, kg$ is moving at a speed of $30\, m/s$. Brakes are applied to bring the car to rest. If the frictional force between the tyres and the road surface is $5000\, N$,the car will come to rest in ........ $s$.

Which of the following is correct when a person walks on a rough surface?

$A$ 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:

The coefficient of friction between the block of mass ${M_1}$ and the surface is $\mu$. When the system is released,it moves with acceleration. What mass $m$ should be placed on the block ${M_1}$ so that the system moves with a constant velocity?