A particle moving with a uniform acceleration travels $24 \,m$ and $64\, m$ in the first two consecutive intervals of $4 \,sec$ each. Its initial velocity is............$m/sec$

Which of the following represents uniformly accelerated motion?

A rocket is moving in a gravity free space with a constant acceleration of $2 \ ms ^{-2}$ along $+x$ direction (see figure). The length of a chamber inside the rocket is $4 \ m$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3 \ ms ^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2 \ ms ^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is:

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

A bullet fired into a fixed target loses half of its velocity after penetrating $3\,cm$ . How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?.......$cm$

A metro train starts from rest and in five seconds achieves $108\, km/h$. After that it moves with constant velocity and comes to rest after travelling $45\, m$ with uniform retardation. If total distance travelled is $395\,m$, then total time of travelling is.......$sec$