A person walks up a stationary escalator in $t_1$ second. If he remains stationary on the escalator, then it can take him up in $t_2$ second. If the length of the escalator is $L$, then
(a) Determine the speed of man with respect to the escalator.
(b) Determine the speed of the escalator.
(c) How much time would it take him to walk up the moving escalator?

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. $\left(g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$