A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x -$ axis. Identify all figures that correctly represent the motion qualitatively. ($a =$ acceleration, $v =$ velocity, $x =$ displacement, $t =$ time)
$a, b, c$
$a$
$b, c$
$a, b, d$
The motion of a body is given by the equation $\frac{{dv(t)}}{{dt}} = 6.0 - 3v(t)$. where $v(t)$ is speed in $m/s$ and $t$ in $\sec $. If body was at rest at $t = 0$
The velocity $u$ and displacement $r$ of a body are related as $u^2 = kr$, where $k$ is a constant. What will be the velocity after $1\, second$ ? (Given that the displacement is zero at $t = 0$)
The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement