$A$ 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 $10 \, kg$ is placed on a rough horizontal surface having a coefficient of friction $\mu = 0.5$. If a horizontal force of $100 \, N$ is acting on it,then the acceleration of the block will be ....... $m/s^2$.

In the given figure,the acceleration of the block of mass $M = \frac{10}{3} \, kg$ is (given $g = 10 \, ms^{-2}$,$\mu = \frac{1}{3}$,$F = 50 \, N$,and $\theta = \sin^{-1}(\frac{3}{5})$):

The power required for an engine to maintain a constant speed of $50 \,m \,s^{-1}$ for a train of mass $3 \times 10^6 \,kg$ on rough rails is (The coefficient of kinetic friction between the rails and wheels of the train is $0.05$ and acceleration due to gravity $= 10 \,m \,s^{-2}$).

$A$ 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 $g = 10 \, m/s^2$)

$A$ body of mass $40\,kg$ resting on a rough horizontal surface is subjected to a force $P$ which is just enough to start the motion of the body. If $\mu_{s} = 0.5$,$\mu_{k} = 0.4$,$g = 10\,m/s^2$,and the force $P$ is continuously applied on the body,then the acceleration of the body is $.........\,m/s^2$.