Consider a vehicle moving with a velocity $54 \,km/h$. At a distance of $400 \,m$ from the traffic light, brakes are applied. The acceleration of the vehicle after the application of brakes is $-0.3 \,m/s^2$. The vehicle's position relative to the traffic light is: (in $\,m$)

$A$ 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

If the displacement of a particle varies with time as $\sqrt{x} = t + 7$,then

$A$ man of height $h$ is walking away from a street lamp with a constant speed $v$. The height of the street lamp is $3h$. The rate at which the length of the man's shadow is increasing when he is at a distance $10h$ from the base of the street lamp is:

$A$ bus moving along a straight highway with a speed of $72 \,km/h$ is brought to a halt within $4 \,s$ after applying the brakes. The distance travelled by the bus during this time (assume the retardation is uniform) is . . . . . . $m$.

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