A train starting from rest travels the first part of its journey with constant acceleration $a$ , second part with constant velocity $v$ and third part with constant retardation $a$ , being brought to rest. The average speed for the whole journey is $\frac{{7v}}{8}$. The train travels with constant velocity for $...$ of the total time

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 body starts with an initial velocity of $10\,ms ^{-1}$ and is moving along a straight line with constant acceleration. When the velocity of the particle is $50\,ms ^{-1}$, the acceleration is reversed in direction. The velocity of the particle when it again reaches the starting point is $............\,m/s^{-1}$

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

If the velocity of a particle is $(10 + 2t^2) m/s$, then the average acceleration of the particle between $2s$ and $5s$ is..........$m/s^2$

Position $x$ of a particle at any instant is related with velocity as $v = \sqrt {2x + 9}$ . The particle starts from origin. Then initial acceleration and velocity are