$A$ ball is dropped on the floor from a height of $20 \ m$. It rebounds to a height of $5 \ m$. The ball remains in contact with the floor for $1 \ s$. The average acceleration during contact is (acceleration due to gravity $g = 10 \ m/s^2$): (in $m/s^2$)

$A$ vehicle without passengers is moving on a frictionless horizontal road with velocity $u$ and can be stopped in a distance $d$. Now,$40\%$ of its weight is added. If the retardation remains the same,what is the stopping distance at velocity $u$?

In which of the following cases is the contact force between $A$ and $B$ maximum? (Given: $m_A = m_B = 1 \ kg$)

$Assertion$: Use of ball bearings between two moving parts of a machine is a common practice.
$Reason$: Ball bearings reduce vibrations and provide good stability.

$A$ block of mass $m$ is lying on a rough inclined plane having an inclination $\alpha = \tan^{-1}(\frac{1}{5})$. The inclined plane is moving horizontally with a constant acceleration of $a = 2 \text{ ms}^{-2}$ as shown in the figure. The minimum value of the coefficient of friction,so that the block remains stationary with respect to the inclined plane,is (Take $g = 10 \text{ ms}^{-2}$):

The masses of blocks $A$ and $B$ are $m$ and $M$ respectively. Between $A$ and $B$,there is a constant frictional force $F$ and $B$ can slide on a smooth horizontal surface. $A$ is set in motion with velocity $v_0$ while $B$ is at rest. What is the distance moved by $A$ relative to $B$ before they move with the same velocity?