$A$ body is moving with a uniform velocity of $8\,m/s$. When the body just crosses another body,the second body starts from rest and moves with a uniform acceleration of $4\,m/s^2$. The time after which the two bodies meet will be $...........\,s$.

$A$ body travels in a straight line from point $A$ to point $B$ with an initial velocity zero and uniform acceleration, covering $1 \,m$ during the first second and $39 \,m$ during the last second. The distance between $A$ and $B$ in metre is

For a train engine moving with a speed of $20 \; m/s$,the driver must apply brakes at a distance of $500 \; m$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance,the train engine would cross the station with a speed of $\sqrt{x} \; m/s$. The value of $x$ is $..............$ (Assuming the same retardation is produced by the brakes).

$A$ bullet from a gun is fired into a rectangular wooden block with velocity $u$. When the bullet travels $24\,cm$ through the block along its length horizontally,the velocity of the bullet becomes $\frac{u}{3}$. It then further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is $........\,cm$.

$A$ small block slides down on a smooth inclined plane,starting from rest at time $t=0$. Let $S_{n}$ be the distance travelled by the block in the interval $t=n-1$ to $t=n$. Then,the ratio $\frac{S_{n}}{S_{n+1}}$ is

$A$ body of mass $1\,kg$ crosses a point $O$ with a velocity $60\,ms^{-1}$. $A$ force of $10\,N$ directed towards $O$ begins to act on it. It will again cross $O$ in ......... $\sec$.