Two trains, which are moving along different tracks in opposite directions, are put on the same track by mistake. On noticing the mistake, when the trains are $300 \, m$ apart, the drivers start slowing down the trains. The graphs given below show the decrease in their velocities as a function of time. The separation between the trains when both have stopped is: (in $ \, m$)

The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\,[1 - {e^{ - bt}}]$. Then the velocity of the particle is

$A$ train starting from rest accelerates uniformly for $100\,s,$ then comes to a stop with a uniform retardation in the next $200\,s.$ During the motion,it covers a distance of $3\,km.$ Choose the wrong option.

The position of a particle related to time is given by $x = (5t^2 - 4t + 5) \, m$. The magnitude of velocity of the particle at $t = 2 \, s$ will be $........... \, ms^{-1}$.

The figure shows a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion,give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A, B, C$ and $D$?

The figure shows a velocity-time graph of a particle moving along a straight line. Identify the region in which the magnitude of the rate of change of velocity $\left| \frac{\Delta \vec{v}}{\Delta t} \right|$ of the particle is maximum.