A particle moves with an initial velocity $v_0$ and retardation $\mathrm{\beta }v$, where, $v$ is its velocity at any time $t$ and $\mathrm{\beta }$ is a positive constant. Then,

Acceleration versus velocity graph of a particle moving in a straight line starting from rest is as shown in the figure. The corresponding velocity-time graph would be

Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are $300 \mathrm{m}$ apart. Graphs given below show their velocities as a function of time as the trains slow down. What is the separation between the trains (in metre) when both have stopped?