The velocity $v$ of a particle as a function of its position $x$ is expressed as $v = \sqrt{c_1 - c_2 x}$,where $c_1$ and $c_2$ are positive constants. The acceleration of the particle is

$A$ body starts from rest with uniform acceleration $a$. Its velocity after $n \ s$ is $v$. The displacement of the body in the last $3 \ s$ is: (Assume total time of journey is $n \ s$)

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3} \ m/s^2$ in the third second is:

$A$ body starts moving from rest with constant acceleration. It covers a displacement $S_1$ in the first $(p-1)$ seconds and $S_2$ in the first $p$ seconds. The total displacement $S_1+S_2$ will be covered in time:

Two points move in the same straight line starting at the same moment from the same point. The first moves with constant velocity $u$ and the second with constant acceleration $f$. During the time that elapses before the second catches the first,the greatest distance between the particles is $........$

$A$ $100\, m$ long train is moving with a uniform velocity of $45\, km/hr$. The time taken by the train to cross a bridge of length $1\, km$ is.........$s$