$A$ particle starts moving with acceleration $2 \, m/s^2$. The distance travelled by it in the $5^{\text{th}}$ half-second is ....... $m$. (in $.25$)

$A$ lift performs the first part of its ascent with uniform acceleration $a$ and the remaining with uniform retardation $2a$. If $t$ is the total time of ascent,find the total height of the shaft.

$A$ car moving along a straight line is brought to a stop within a distance of $200 \,m$ and in a time of $10 \,s$. The initial speed of the car is (in $\,ms^{-1}$)

Two trains travelling on the same track are approaching each other with equal speeds of $40\ m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\ km$ apart. Assuming the decelerations to be uniform and equal,the value of the deceleration to barely avoid collision should be..........$m/s^2$.

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).

$A$ body starts from rest and moves with constant acceleration for $t$ seconds. It travels a distance $x_{1}$ in the first half of the time and $x_{2}$ in the next half of the time. Then: