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.........$s$

The velocity of the bullet becomes one third after it penetrates $4\,cm$ in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at $(4+x)\,cm$ inside the block. The value of $x$ is$.....$

Position time graph of a particle moving along straight line is shown which is in the form of semicircle starting from $t=2$ to $t=8 \,s$. Select correct statement

A particle initially at rest moves along the $x$-axis. Its acceleration varies with time as $a=4\,t$. If it starts from the origin, the distance covered by it in $3\,s$ is $...........\,m$

The relation between time and distance is $t = \alpha {x^2} + \beta x$, where $\alpha $ and $\beta $ are constants. The retardation is

The velocity $(v)$ of a particle moving along $x$-axis varies with its position $x$ as shown in figure. The acceleration $(a)$ of particle varies with position $(x)$ as