The maximum possible acceleration of a train moving on a straight track is $10\  m/s^2$ and maximum possible retardation is $5 \ m/s^2.$ If maximum achievable speed of train is $10\ m/s$ then minimum time in which train can complete a journey of $135\ m$ starting from rest and ending at rest, is………$s$

A particle moves in a straight line and its position $x$ at time $t$ is given by $x^2=2+t$. Its acceleration is given by

The graph shows the variation with time $t$ of velocity $v$ of an object moving along a straight line. $a-t$ graph will be

A particle of mass $m$ moves on the x-axis as follows : it starts from rest at $t = 0$ from the point $x = 0$ and comes to rest at $ t= 1$ at the point $x = 1$. No other information is available about its motion at intermediate time $(0 < t < 1)$. If $\alpha $ denotes the instantaneous acceleration of the particle, then

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