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)
$a, b, c$
$a$
$b, c$
$a, b, d$
A man goes $10\,m $ towards North, then $ 20\,m$ towards east then displacement is........$m$
A particle moves for $8\, seconds$. It first accelerates from rest and then retards to rest. If the retardation be $3\, times$ the acceleration, then time for which it accelerates will be
The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time $t$ will be
A car accelerates from rest at a constant rate $\alpha $ for some time, after which it decelerates at a constant rate $\beta $ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is
Starting from rest, acceleration of a particle is $a = 2(t - 1).$ The velocity of the particle at $t = 5\,s$ is.........$m/sec$