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

Draw the $x\to t$ graphs for positive, negative and zero acceleration.

Position $x$ of a particle at any instant is related with velocity as $v = \sqrt {2x + 9}$ . The particle starts from origin. Then initial acceleration and velocity are

The displacement $(x)$ of a particle depends on time $t$ as $x=\alpha t^2-\beta t^3$. Choose the incorrect statements from the following.

A particle is moving with constant acceleration $'a'.$ Following graph shows $v^{2}$ versus $x$ (displacement) plot. The acceleration of the particle is $......{m} / {s}^{2}$

The displacement of a particle, moving in a straight line, is given by $s = 2{t^2} + 2t + 4$ where $s$ is in metres and $t$ in seconds. The acceleration of the particle is........$ms^{-2}$