$A$ body of mass $0.5 \ kg$ is supplied with a power $P$ (in watt) which varies with time $t$ (in second) as $P = 3t^2 + 3$. If the velocity of the body at time $t = 0$ is zero,then the velocity of the body at time $t = 3 \ s$ is (in $ms^{-1}$)

$A$ block of mass $M = 1 \ kg$ is released from rest at the top of a smooth track of radius $R = 40 \ m$. The block slides along the track without toppling,and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point $Q$ (where the radius makes an angle of $30^{\circ}$ with the horizontal),as shown in the figure,is $150 \ J$. (Take the acceleration due to gravity,$g = 10 \ m s^{-2}$)
$1.$ The speed of the block when it reaches the point $Q$ is:
$(A) 5 \ m s^{-1}$ $(B) 10 \ m s^{-1}$ $(C) 10\sqrt{3} \ m s^{-1}$ $(D) 20 \ m s^{-1}$
$2.$ The magnitude of the normal reaction that acts on the block at the point $Q$ is:
$(A) 7.5 \ N$ $(B) 8.6 \ N$ $(C) 11.5 \ N$ $(D) 22.5 \ N$
Give the answers for question $1$ and $2$.

Two bodies $A$ and $B$ of masses $20 \ kg$ and $5 \ kg$ respectively are at rest. Due to the action of a force of $40 \ N$ separately,if the two bodies acquire equal kinetic energies in times $t_A$ and $t_B$ respectively,then $t_A: t_B=$

Block $A$ of mass $m$ is hanging from a vertical spring of spring constant $k$ and is at rest. Block $B$ of mass $m$ strikes block $A$ with velocity $v$ and sticks to it. The velocity $v$ for which the spring just attains its natural length is:

Two massless strings of length $5\, m$ hang from the ceiling very near to each other as shown in the figure. Two balls $A$ and $B$ of masses $0.25\, kg$ and $0.5\, kg$ are attached to the strings. The ball $A$ is released from rest at a height of $0.45\, m$ as shown in the figure. The collision between the two balls is completely elastic. Immediately after the collision,the kinetic energy of ball $B$ is $1\, J$. The velocity of ball $A$ just after the collision is

$A$ ball of mass $m$ falls vertically from a height $h$ and collides with a block of equal mass $m$ moving horizontally with a velocity $v$ on a surface. The coefficient of kinetic friction between the block and the surface is $0.2$,while the coefficient of restitution $e$ between the ball and the block is $0.5$. There is no friction acting between the ball and the block. The velocity of the block decreases by: