Two cars are moving towards each other on a straight road with accelerations $5 \mathrm{m} {\mathrm{s}}^{-2}$ and $15 \mathrm{m} {\mathrm{s}}^{-2}$. At a certain instant, their separation is $400 \mathrm{m}$ and their velocities are$10 \mathrm{m} {\mathrm{s}}^{-1}$ and $20 \mathrm{m} {\mathrm{s}}^{-1}$. How long will it take for the cars to collide ?

A boat goes from point  $A$ to $B$ downstream of a river flowing with speed  $6 \mathrm{km} {\mathrm{h}}^{-1}$ and then comes back to point $A$. If time taken in upstream journey is double of that in downstream journey then speed of boat in still water is

Graph of  $\left(\frac{1}{V}\right)$ versus $x$ for a particle under motion is shown in figure, where $v$ is velocity and $x$ is position. Find the time taken by particle to move from $x=4 \mathrm{m}$ to $x=12 \mathrm{m}$.