$A$ 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 ........ $s$.

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 $1 \,kg$ is moving with a velocity $10 \,ms^{-1}$ on a horizontal rough surface having a coefficient of kinetic friction $0.4$. If the constant force is removed, the body comes to rest in a time (Acceleration due to gravity $g = 10 \,ms^{-2}$). (in $\,s$)

$A$ body of weight $50 \,N$ placed on a horizontal surface is just moved by a force of $28.2 \,N$ applied at an angle of $45^\circ$ with the horizontal. The frictional force and the normal reaction are

What is rolling friction? Write the laws of rolling friction. Define the coefficient of rolling friction.

$A$ stationary body of mass $m$ is slowly lowered onto a massive platform of mass $M$ $(M \gg m)$ moving at a speed $V_p = 4 \, m/s$ as shown in the figure. How far will the body slide along the platform (in $, m$)? (Given: $\mu = 0.2$ and $g = 10 \, m/s^2$)