A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ -direction. Its speed $v(t)$ is depicted by which of  the  following curves ?

If mass of $A = 10\,\,kg$, coefficient of static friction $= 0.2$, coefficient of kinetic friction = $0.2$. Then mass of $B$ to start motion is

A conveyor belt is moving at a constant speed of $2\, ms^{-1}$. A box is gently dropped on it. The coefficient of friction between them is $\mu  = 0.5$. The distance that the box will move relative to belt before coming to rest on it, (taking $g = 10\, ms^{-2}$) is  ........  $m$.

Meena applies the front brakes, while riding on her bicycle along a flat road. The force that slows her bicycle is provided by the

A block of mass $2 kg$ slides down an incline plane of inclination $30^o$. The coefficient of friction between block and plane is $0.5$. The contact force between block and plank is :

When a bicycle is in motion, the force of friction exerted by the ground on the two wheels is such that it acts