$A$ rifle bullet loses $(1/20)^{th}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

$A$ train accelerates from rest at a constant rate $\alpha$ for distance $x_1$ and time $t_1$. After that,it retards to rest at a constant rate $\beta$ for distance $x_2$ and time $t_2$. Which of the following relations is correct?

The acceleration of an object increases with time as $a = bt$. The object starts from the origin with an initial velocity $v_0$. Find the distance traveled by the object in time $t$.

$A$ 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 $........\,cm$.

$A$ body starting from rest moves with an acceleration of $\frac{5}{4} \,ms^{-2}$. The distance travelled by the body in the third second is:

$A$ body $A$ starts from rest with an acceleration $a_{1}$. After two seconds,another body $B$ starts from rest with an acceleration $a_{2}$. If they travel equal distances in the fifth second after the start of $A$,the ratio $a_{1}: a_{2}$ will be equal to: