Two towns $A$ and $B$ are connected by regular bus service with a bus leaving in either direction every $T$ $\min$. A man cycling with a speed of $20 \mathrm{km}{ \mathrm{h}}^{-1}$ in the direction $A$ to $B$ notices that a bus goes past him every $18$$\min$ in the direction of his motion and every $6 \min$ in the opposite direction. What is the period $T$ of the bus service and with what speed (assumed constant) do the buses ply on the road?

A police van moving on a highway with a speed of $30 \mathrm{km}{ \mathrm{h}}^{-1}$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192 \mathrm{km}{ \mathrm{h}}^{-1}$. If the muzzle speed of the bullet is $150 \mathrm{m} {\mathrm{s}}^{-1}$, with what speed does the bullet hit the thief's car?

On a two-lane road, car $A$ is travelling at a speed of $36 \mathrm{km}{ \mathrm{h}}^{-1}$. Two cars $B$ and $C$ approach car $A$ in opposite directions with a speed of $54 \mathrm{km}{ \mathrm{h}}^{-1}$. At a certain instant, when the distance $AB$is equal to $AC$, both $1 \mathrm{km}, B$ decided to overtake $A$ before $C$ does. What minimum acceleration of car $B$ is required to avoid an accident?

Two particles $A$ and$B$ are thrown vertically upward with velocity, $5 \mathrm{m}$ ${\mathrm{s}}^{-1}$ and $10 \mathrm{m}{ \mathrm{s}}^{-1}$, respectively $(g=10$$\mathrm{m} {\mathrm{s}}^{-2}$ ). Find separation between them after $1 \mathrm{s}$.

A ball is thrown downwards with a speed of $20{ \mathrm{m} \mathrm{s}}^{-1}$ from the top of a building $150 \mathrm{m}$ high and simultaneously another ball is thrown vertically upwards with a speed of $30{ \mathrm{m} \mathrm{s}}^{-1}$ from the foot of the building. Find the time after which both the balls will meet. $\left(g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$