Starting from rest,the acceleration of a particle is given by $a = 2(t - 1)$. The velocity of the particle at $t = 5 \, s$ is ......... $m/s$.

$A$ particle moves for $8 \, s$. It first accelerates from rest and then retards to rest. If the retardation is $3 \, times$ the acceleration, then the time for which it accelerates is: (in $s$)

$A$ particle is moving in a straight line. The variation of position $x$ as a function of time $t$ is given as $x = (t^3 - 6t^2 + 20t + 15) \ m$. The velocity of the body when its acceleration becomes zero is ........... $m/s$.

$A$ bullet fired into a fixed target loses half of its velocity after penetrating $3\,cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion? (in $cm$)

If the displacement of a particle varies with time as $\sqrt{x} = t + 7$,then

$A$ particle with initial velocity $v_0$ moves with constant acceleration $a$ in a straight line. Find the distance travelled in the $n^{th}$ second.