The displacement of a particle moving in a straight line depends on time as $x = \alpha t^3 + \beta t^2 + \gamma t + \delta$. The ratio of initial acceleration to its initial velocity depends on:

Two trains '$A$' and '$B$' of length '$l$' and '$4l$' are travelling into a tunnel of length '$L$' on parallel tracks from opposite directions with velocities $108\,km/h$ and $72\,km/h$,respectively. If train '$A$' takes $35\,s$ less time than train '$B$' to cross the tunnel,then the length '$L$' of the tunnel is $...........\,m$. (Given $L = 60l$)

$A$ ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2$. Neglecting subsequent motion and air resistance,its velocity $v$ varies with the height $h$ above the ground as:

$A$ street car moves rectilinearly from station $A$ to the next station $B$ with an acceleration varying according to the law $a = (b - cx)$,where $b$ and $c$ are constants and $x$ is the distance from station $A$. The distance between the two stations and the maximum velocity are:

$A$ parachutist drops freely from an aeroplane for $10\,s$ before the parachute opens. Then he descends with a net retardation of $2.5\,m/s^2$. If he bails out of the plane at a height of $2495\,m$ and $g = 10\,m/s^2$,his velocity on reaching the ground will be .......$m/s$.

At time $t=0$,a car moving along a straight line has a velocity of $16 \; m/s$. It slows down with an acceleration of $a = -0.5t \; m/s^2$,where $t$ is in seconds. Mark the correct statement$(s)$.