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

Displacement $(x)$ of a particle is related to time $(t)$ as:

$x = at + bt^2 -ct^3$

where $a, b$ and $c$ are constants of the motion. The velocity of the particle when its acceleration is zero is given by

The initial velocity of a particle moving along $x$-axis is $u$ (at $t=0$ and $x=0$ ) and its acceleration $a$ is given by $a=k x$. Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?

The initial velocity of a particle is $u\left(\right.$ at $t=0$ ) and the acceleration a is given by $\alpha t^{3 / 2}$. Which of the following relations is valid?

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

The velocity $(v)$-time $(t)$ graph for a particle moving along $x$-axis is shown in the figure. The corresponding position $(x)$ - time $(t)$ is best represented by