$A$ car is moving with a speed of $150 \ km/h$ and after applying the brakes,it travels $27 \ m$ before it stops. If the same car is moving with a speed of one-third of the initial speed,then it will stop after traveling how many meters?

The two ends of a train moving with constant acceleration pass a certain point with velocities $u$ and $3u$. The velocity with which the middle point of the train passes the same point is ........... $u$.

$A$ body travels $102.5 \ m$ in the $n^{\text{th}}$ second and $115.0 \ m$ in the $(n+2)^{\text{th}}$ second. The acceleration is: (in $m/s^2$)

$A$ 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

The relation between time $t$ and distance $x$ of a particle is $t = ax^2 + bx$, where $a$ and $b$ are constants. If $v$ is the velocity of the particle, then its acceleration is

Two cars $A$ and $B$ initially at rest are moving in the same direction with accelerations $a_1$ and $a_2$ respectively. After a certain time $t$, they achieve velocities $v_1$ and $v_2$ respectively and are separated by a distance of $50 \ m$. If $(a_1 - a_2) = 4 \ m \ s^{-2}$, then the quantity $(v_1 - v_2)$ will be: (in $m \ s^{-1}$)