$A$ body is moved from rest along a straight line by a machine delivering constant power. The ratio of displacement and velocity $(s/v)$ varies with time $t$ as :

$A$ car travelling at a speed of $30 \, km/h$ is brought to a halt in $8 \, m$ by applying brakes. If the same car is travelling at $60 \, km/h$,it can be brought to a halt with the same braking force in ............... $m$.

$A$ body of mass $2 \,kg$ thrown vertically from the ground with a velocity of $8 \,ms^{-1}$ reaches a maximum height of $3 \,m$. The work done by the air resistance is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,J$)

$A$ block moving horizontally on a smooth surface with a speed of $40 \, m/s$ splits into two equal parts. If one of the parts moves at $60 \, m/s$ in the same direction,then the fractional change in the kinetic energy will be $x: 4$ where $x = ..... .$

Consider a one-dimensional collision involving a body of mass $m_1$ moving in the positive $x$ direction with speed $v_0$ and a second body of mass $m_2$ initially at rest. The collision can be completely inelastic,completely elastic,or partially inelastic. After the collision,$m_1$ moves with velocity $v_1$ and $m_2$ moves with velocity $v_2$. Determine the range of final velocity $v_1$ for the following cases:
$(A)$ If $m_1 > m_2$
$(B)$ If $m_1 < m_2$

Two statements are given below. Select the option that correctly explains both statements.
Statement-$1$: In a perfectly elastic collision between two particles moving in the same direction,they do not lose all their energy.
Statement-$2$: The principle of conservation of momentum is valid for all types of collisions.