The motion of a particle along a straight line is described by the equation $x = 8 + 12t - t^3$,where $x$ is in meters and $t$ is in seconds. The retardation of the particle when its velocity becomes zero is .......... $m/s^2$.

The velocity of a car accelerating uniformly increases from $20 \ m/s$ to $80 \ m/s$ while covering a distance of $200 \ m$. The time taken is $.... \ s$.

$A$ 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......$m/sec$.

An engine of a train,moving with uniform acceleration,passes a signal post with velocity $u$ and the last compartment passes the same signal post with velocity $v$. The velocity with which the middle point of the train passes the signal post is

Two cars leave one after the other and travel with an acceleration of $0.4\, m/s^2$. Two minutes after the departure of the first,the distance between the cars becomes $1.9\, km$. The time interval between the departures of the cars is ........$s$.

$A$ car is moving along a straight road with uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance $s$ with velocities $30\; km/h$ and $40\; km/h$ respectively. Find the velocity of the car midway between $P$ and $Q$.